Luke Moore's fifth goal of the season rescued a point for Swansea against Norwich at Carrow Road.
Michael Turner put the Canaries ahead early in the second half after Robert Snodgrass equalised Michu's opener for Swansea.
And the Spanish midfielder missed a glorious chance to give Swansea all three points in added time.
The result leaves Norwich in 13th place, still only five points clear of the relegation places.
It was Norwich's fifth draw in their last six home matches, and their continued failure to open a comfortable gap over the teams in the bottom three will be a worry for manager Chris Hughton.
For much of the second half they looked the stronger team after Swansea dominated possession for the opening 50 minutes.
But the Canaries could not find a decisive third goal, and Swansea should have taken all three points when top scorer Michu fired over from seven yards in stoppage time.
It was another entertaining match for the neutral observer - the last four matches between these sides in the Premier League have now produced 20 goals.
Midfielder Leon Britton was left out of the Swansea line-up following the birth of his twin sons.
Manager Michael Laudrup gave Moore his third start of the season, while Norwich had goalkeeper Mark Bunn back in action after missing one game following his red card against Sunderland.
And they were quickly in action as Bunn saved from Moore after Michu's pass had put the striker into a little space at the edge of the 18-yard box.
And Michu had the ball in the back of the net, but the goal was ruled out because of Moore's foul on Jonathan Howson.
- Michu has now scored three times in the Premier League against Norwich City this season; only versus QPR (4) has he netted more.
- Robert Snodgrass' goal was his first goal at Carrow Road for Norwich City, after having netted each of his previous five for the club away from home.
- Luke Moore has now scored in three of his last four Premier League appearances.
Bunn was forced to leave the field with a groin injury in the 15th minute, with Lee Camp taking over in goal.
The Canaries' best chance fell to Michael Turner after Snodgrass had made inroads on the Swansea left - Michel Vorm saving well from the defender's scuffed half-volley from six yards.
In fact, Snodgrass had a good argument for a penalty in the build-up as he appeared to be pushed by Wayne Routledge.
Swansea dominated possession and took the lead in the 35th minute as Nathan Dyer, Chico Flores and Jonathan De Guzman teed up Michu who blasted his 21st goal of the season into the roof of the net.
Dyer fluffed a golden chance a few minutes later, and Swansea were immediately punished as Kei Kamara freed Elliott Bennett whose cross was headed into an open goal by the unmarked Snodgrass.
The goal gave Norwich new impetus, and they finished the half stronger with Kamara firing a shot over the bar.
Swansea started the second half in complete control, with Camp forced into a point-blank save from Moore after Wayne Routledge had outfoxed the defence, but Norwich made light of their lack of possession to stun the Swans.
Bennett was again the provider, his right-footed free kick catching the Swansea defence flat-footed, and Michael Turner fired in a fine shot on the half-volley to give the Canaries the lead.
Swansea were rocking, with the home side displaying the greater hunger.
But the game swung again as the visitors manufactured an opening for Moore, who fired in his fifth goal of the season from six yards after Angel Rangel headed across the box.
Both teams pressed for the win in the dying minutes, with Michu's added-time miss the closest either side came.
Norwich manager Chris Hughton:
"We wanted a win but nothing changes, we still have to get enough points from the six remaining matches to make sure we're secure.
"Their camp might look at it a little bit differently, but I thought on the balance of play it was a fair result. I couldn't fault the team for their endeavour, we got ourselves in scoring positions but unfortunately we conceded two soft goals.
"We spoke about the goals we conceded, which I felt were poor to concede, but we gave ourselves opportunities to score and that is what we have found difficult."
Swansea manager Michael Laudrup:
"We dominated completely for the first 30 minutes, [it was] a great goal from Michu. And then out of nowhere we let Norwich come back into the game a couple of bad decisions and suddenly they equalised.
"We started the first 10 minutes of the second half well and then suddenly we're 2-1 down because of some misunderstanding or bad marking at a set-piece.
"I think it's important to come back with a positive result because... we have two weeks now before the next game against Southampton, which for me we have to win if we want to end up in the top 10."
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Live Text Commentary
Full Time The referee blows his whistle to end the game.90:00 +2:39
The free kick is swung in right-footed by Jonathan de Guzman, free kick awarded for an unfair challenge on Michael Turner by Luke Moore. Lee Camp takes the free kick.90:00 +2:39 Booking
Booking Booking for Alexander Tettey.90:00 +2:28
Free kick awarded for a foul by Alexander Tettey on Roland Lamah.90:00 +1:42
Bradley Johnson fouled by Luke Moore, the ref awards a free kick. Free kick taken by Javier Garrido.90:00 +0:55
The ball is swung over by Pablo Hernandez, Close range effort by Miguel Michu clears the crossbar.90:00 +0:19
A cross is delivered by Pablo Hernandez, Michael Turner manages to make a clearance.89:57
Robert Snodgrass takes a shot. Miguel Michu gets a block in.88:48
Direct strike on goal from the free kick comes in from Robert Snodgrass.88:48 Booking
Booking Jonathan de Guzman receives a caution for unsporting behaviour.88:41
Kei Kamara fouled by Jonathan de Guzman, the ref awards a free kick.88:28
Centre by Jonathan de Guzman, save by Lee Camp.85:43
Michel Vorm restarts play with the free kick.85:43 Booking
Booking Grant Holt goes into the referee's book.85:38
Grant Holt concedes a free kick for a foul on Chico.85:22
Grant Holt takes a shot. Angel Rangel manages to make a clearance.84:27
Shot on goal comes in from Jonathan de Guzman from the free kick, save by Lee Camp.84:27 Booking
Booking Michael Turner is shown a yellow card for unsporting behaviour.84:15
Free kick awarded for an unfair challenge on Miguel Michu by Michael Turner.81:21
Close range shot by Miguel Michu goes wide of the left-hand upright.
Angel Rangel takes the free kick.80:05 Substitution
Substitution Alexander Tettey comes on in place of Jonathan Howson.80:05
Foul by Grant Holt on Chico, free kick awarded.79:04 Substitution
Substitution Grant Holt comes on in place of Wes Hoolahan.79:04
Russell Martin produces a left-footed shot from the edge of the area and misses to the left of the goal.74:53
The assist for the goal came from Angel Rangel.74:53 Goal scored
Goal! - Luke Moore - Norwich 2 - 2 Swansea Luke Moore fires in a goal from close range low into the middle of the goal. Norwich 2-2 Swansea.74:50
The ball is sent over by Dwight Tiendalli.74:03
Outswinging corner taken from the right by-line by Jonathan de Guzman, Miguel Michu takes a shot. Clearance by Wes Hoolahan.74:03 Substitution
Substitution Roland Lamah replaces Nathan Dyer.73:42
The ball is crossed by Pablo Hernandez, Luke Moore takes a shot. Save by Lee Camp.72:54
Wes Hoolahan crosses the ball, Michel Vorm makes a save.72:48
The ball is delivered by Robert Snodgrass, clearance made by Chico.71:02
Shot by Wes Hoolahan from outside the box goes high over the crossbar.70:37
Chico concedes a free kick for a foul on Robert Snodgrass. Free kick crossed by Elliott Bennett, clearance made by Angel Rangel.69:54
Elliott Bennett sends in a cross, Ashley Williams makes a clearance.68:21
Robert Snodgrass crosses the ball from the free kick left-footed from right channel, save by Michel Vorm.68:21 Booking
Booking The referee books Ashley Williams for unsporting behaviour.68:09
Free kick awarded for a foul by Ashley Williams on Kei Kamara.67:20
Angel Rangel crosses the ball.67:06
The ball is sent over by Luke Moore, clearance made by Michael Turner.65:46
The ball is sent over by Elliott Bennett. Kei Kamara is caught offside. Michel Vorm takes the indirect free kick.63:10
Javier Garrido delivers the ball from the free kick left-footed from left channel, clearance made by Chico.63:10 Substitution
Substitution (Swansea) makes a substitution, with Angel Rangel coming on for Ben Davies.63:10 Substitution
Substitution Pablo Hernandez on for Wayne Routledge.63:10
Nathan Dyer gives away a free kick for an unfair challenge on Robert Snodgrass.62:29
Elliott Bennett delivers the ball.61:39
The ball is crossed by Ben Davies, Sung-Yeung Ki takes a shot. Comfortable save by Lee Camp.60:54
The ball is delivered by Chico, Michael Turner manages to make a clearance.59:35
Assist by Elliott Bennett.59:35 Goal scored
Goal! - Michael Turner - Norwich 2 - 1 Swansea Michael Turner finds the back of the net with a goal from close range to the top left corner of the goal. Norwich 2-1 Swansea.58:58
Free kick awarded for a foul by Ashley Williams on Kei Kamara. The ball is sent over by Elliott Bennett,57:45
Jonathan Howson delivers the ball, clearance by Dwight Tiendalli.56:33
Free kick awarded for an unfair challenge on Jonathan Howson by Ben Davies. Lee Camp takes the free kick.54:47
Free kick awarded for an unfair challenge on Jonathan Howson by Wayne Routledge. Free kick crossed left-footed by Robert Snodgrass, save made by Michel Vorm.54:24
Russell Martin takes a shot from 25 yards. Save made by Michel Vorm.54:18
A cross is delivered by Robert Snodgrass.53:25
The ball is sent over by Dwight Tiendalli.52:41
The ball is delivered by Nathan Dyer, clearance made by Michael Turner.51:11
Foul by Sebastien Bassong on Miguel Michu, free kick awarded. Jonathan de Guzman takes the direct free kick.50:31
Ben Davies produces a cross, Effort from inside the six-yard box by Miguel Michu goes wide left of the target.49:37
Luke Moore takes a shot. Lee Camp makes a brilliant save. Corner taken by Jonathan de Guzman, clearance by Russell Martin.48:58
Ben Davies delivers the ball, clearance made by Michael Turner.46:21
Elliott Bennett crosses the ball.45:01
The match restarts for the second half.45:00 +3:12 Half time
Half Time The ref blows to signal half-time.45:00 +1:46
Miguel Michu takes a shot. Blocked by Russell Martin.45:00 +0:17
Kei Kamara takes a shot from just inside the penalty box which clears the bar.43:18
The ball is swung over by Kei Kamara, clearance by Wayne Routledge. Elliott Bennett takes a outswinging corner to the near post, Dwight Tiendalli makes a clearance.43:10
Centre by Wes Hoolahan.42:58
Free kick awarded for an unfair challenge on Elliott Bennett by Chico. Wes Hoolahan restarts play with the free kick.41:19
Wes Hoolahan fouled by Chico, the ref awards a free kick. The free kick is swung in left-footed by Robert Snodgrass, comfortable save by Michel Vorm.39:28
The ball is swung over by Elliott Bennett,39:25
The assist for the goal came from Elliott Bennett.39:25 Goal scored
Goal! - Robert Snodgrass - Norwich 1 - 1 Swansea Robert Snodgrass finds the back of the net with a headed goal from close in. Norwich 1-1 Swansea.38:36
Nathan Dyer produces a right-footed shot from the edge of the area and misses to the left of the target.35:56
Wayne Routledge sends in a cross, clearance by Javier Garrido.35:37
The ball is sent over by Wayne Routledge, clearance made by Javier Garrido.34:14
Assist by Jonathan de Guzman.34:14 Goal scored
Goal! - Miguel Michu - Norwich 0 - 1 Swansea Miguel Michu grabs a goal from inside the area to the top right corner of the goal. Norwich 0-1 Swansea.34:12
Jonathan de Guzman sends in a cross,33:32
Dwight Tiendalli delivers the ball, clearance by Javier Garrido. Short corner taken by Jonathan de Guzman.32:45
Shot from just outside the box by Luke Moore misses to the right of the target.32:32
A cross is delivered by Elliott Bennett, clearance by Chico.32:11
Russell Martin takes a shot. Blocked by Ashley Williams.32:04
Robert Snodgrass delivers the ball, Sung-Yeung Ki makes a clearance.29:51
Shot comes in from Jonathan de Guzman from the free kick, Lee Camp makes a comfortable save.29:51 Booking
Booking Caution for Bradley Johnson.29:42
Foul by Bradley Johnson on Miguel Michu, free kick awarded.29:23
A cross is delivered by Jonathan de Guzman, clearance made by Michael Turner.27:55
Free kick crossed right-footed by Jonathan de Guzman, clearance made by Jonathan Howson.27:55 Booking
Booking The referee cautions Robert Snodgrass for unsporting behaviour.27:44
Robert Snodgrass gives away a free kick for an unfair challenge on Dwight Tiendalli.26:44
The ball is swung over by Elliott Bennett.24:52
Free kick awarded for an unfair challenge on Wayne Routledge by Russell Martin. Ashley Williams takes the free kick.23:16
Jonathan de Guzman takes a inswinging corner from the left by-line played to the near post.22:48
Jonathan de Guzman takes a outswinging corner to the near post, clearance by Michael Turner.22:36
A cross is delivered by Wayne Routledge, clearance made by Russell Martin.22:06
Corner taken left-footed by Robert Snodgrass to the near post, Luke Moore manages to make a clearance.21:46
A cross is delivered by Robert Snodgrass, Michael Turner takes a shot. Save by Michel Vorm.20:47
Direct effort from the free kick comes in from Robert Snodgrass.20:47 Booking
Booking Ben Davies goes into the referee's book for unsporting behaviour.20:38
Elliott Bennett fouled by Ben Davies, the ref awards a free kick.19:55
The ball is crossed by Dwight Tiendalli, save made by Lee Camp.16:51
The referee blows for offside. Lee Camp restarts play with the free kick.16:39
The ball is sent over by Dwight Tiendalli, clearance by Bradley Johnson.13:20 Substitution
Substitution Mark Bunn leaves the field to be replaced by Lee Camp.13:20
The ball is delivered by Dwight Tiendalli.10:36
Nathan Dyer delivers the ball, Javier Garrido manages to make a clearance.9:45
Jonathan Howson fouled by Luke Moore, the ref awards a free kick. Mark Bunn takes the free kick.7:57
Free kick awarded for an unfair challenge on Michael Turner by Luke Moore. Michael Turner takes the indirect free kick.7:32
Effort on goal by Luke Moore from 18 yards. Brilliant save by Mark Bunn.6:15
A cross is delivered by Elliott Bennett.5:30
Shot from just outside the box by Miguel Michu misses to the right of the target.4:11
Jonathan de Guzman challenges Elliott Bennett unfairly and gives away a free kick. Mark Bunn restarts play with the free kick.4:01
Dwight Tiendalli delivers the ball, clearance made by Russell Martin.1:20
Foul by Dwight Tiendalli on Bradley Johnson, free kick awarded. Javier Garrido restarts play with the free kick.0:00
The game begins.
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