Steven Fletcher scored twice on his Sunderland debut to end Swansea's perfect start to the season.
The £14m new signing pounced on Ashley Williams's mistake before curling the ball expertly into the bottom corner.
Swansea responded almost immediately when Wayne Routledge fired home from 10 yards, but Fletcher tapped in at the far post just before half-time.
Michu's powerful header secured a point for the home side, who survived despite Chico's red card 20 minutes from time.
In fact, Swansea continued to look the most likely scorers in the closing stages, having forced Sunderland firmly on the back foot from the start of a dominant second half.
Crucial blocks and well-timed tackles in their own area by visiting defenders denied unchanged Swansea their third consecutive win of the season as Sunderland collected their second point from two games.
Having kept clean sheets in their two opening victories, Swansea's defending looked far from assured as they gifted Sunderland both goals.
Williams was the first offender, horribly miscuing his attempted back-pass, and giving Fletcher a clear run at goal as half-time approached.
As Michel Vorm left his line to close the angle, Fletcher opened up his body, curling the ball around the goalkeeper's outstretched hand just inside the far post.
Swansea's equaliser had all the hallmarks of their intricate passing game as Michu fed Nathan Dyer on the edge of the area. He flicked the ball into Routledge's path, who drove the ball home.
Following a lengthy delay as Swansea left-back Neil Taylor received treatment for a suspected broken ankle, there were six minutes of added time at the end of the first half.
And less than a minute remained when former Wolves striker Fletcher restored Sunderland's lead against the run of play.
Again it was a gift from the home defence as Vorm allowed Sebastian Larsson's cross to reach the far post, where Fletcher forced himself in front of a dithering Chico to tap in from two yards.
Swansea found greater urgency after the break and there was an air of inevitability about Michu's equaliser.
Having seen a powerful header bounce over the bar moments earlier, Michu rose to dispatch Jonathan de Guzman's cross into the bottom corner for his fourth goal of the season.
A third Swansea goal looked a distinct possibility, but Chico's moment of madness halted their momentum.
The defender was given a straight red after clipping Louis Saha's ear with his boot as the Sunderland substitute flicked the ball down the left touchline.
Martin O'Neill's men failed to capitalise, though, and were fortunate that Dyer and De Guzman failed to connect properly with shots in front of goal in an enthralling climax.
But they almost snatched a late winner when Saha's drive was well blocked by substitute Alan Tate after more calamitous defending.
Swansea City manager Michael Laudrup:
"I know we've won two games 5-0 and 3-0, but this game has given me most as a manager because everything was against us from the beginning.
"A very serious injury for Neil [Taylor] after just 10 or 12 minutes, and the first mistake we make they score a goal.
"Then we come back to 1-1 and then passed injury time they score to make it 2-1. Then we came back in the second half and played great football to get the draw."
Sunderland manager Martin O'Neill:
"Darren Bent did very well here and Steven [Fletcher] has come here to score goals.
"But he can also do well for us outside the penalty area, he has a lovely touch, but it was very pleasing for him to get off the mark.
"With all the euphoria of Adam [Johnson] signing for us he was maybe in his shadow a bit, but he is a very good player."
- 01 Vorm
- 03 Taylor (Davies - 20' )
- 04 Chico Dismissed
- 06 Williams Booked
- 22 Rangel
- 07 Britton
- 09 Michu (Ki Sung-Yeung - 78' )
- 12 Dyer
- 15 Routledge (Tate - 73' )
- 20 De Guzman
- 10 Graham
- 25 Tremmel
- 05 Tate
- 33 Davies
- 24 Ki Sung-Yeung
- 26 Agustien
- 17 Shechter
- 19 Moore
- 22 Mignolet
- 16 O'Shea
- 24 Cuellar
- 06 Cattermole (Meyler - 38' )
- 07 Larsson
- 08 Gardner Booked
- 14 Colback
- 21 Johnson
- 23 McClean
- 28 Sessegnon (Campbell - 84' )
- 26 Fletcher (Saha - 67' )
- 20 Westwood
- 12 Kilgallon
- 19 Bramble
- 18 Meyler
- 09 Campbell
- 17 Ji Dong-Won
- 25 Saha
Live Text Commentary
Full Time The final whistle is blown by the referee.90:00 +2:32
Fraizer Campbell takes a shot. Blocked by Alan Tate.90:00 +0:06
Jonathan de Guzman takes the inswinging corner, Craig Gardner manages to make a clearance.89:53
Jonathan de Guzman takes a inswinging corner from the left by-line to the near post, Craig Gardner makes a clearance.85:20
Jonathan de Guzman takes a shot. Blocked by Carlos Cuellar. Shot by Nathan Dyer from deep inside the penalty area misses wide to the left of the target.85:05
The ball is delivered by Nathan Dyer, John O'Shea makes a clearance.83:26
Jonathan de Guzman takes a outswinging corner from the right by-line played to the near post.83:09 Substitution
Substitution Fraizer Campbell is brought on as a substitute for Stephane Sessegnon.82:05
A cross is delivered by James McClean, save by Michel Vorm.79:27
Foul by Stephane Sessegnon on Sung-Yeung Ki, free kick awarded. Direct free kick taken by Alan Tate.78:47
A cross is delivered by Craig Gardner, save made by Michel Vorm.77:26 Substitution
Substitution Sung-Yeung Ki is brought on as a substitute for Miguel Michu.70:18
Free kick crossed right-footed by Sebastian Larsson from left wing.70:18 Substitution
Substitution Alan Tate comes on in place of Wayne Routledge.70:18 Dismissal
Dismissal Chico is shown a red card for serious foul play.69:53
Foul by Chico on Louis Saha, free kick awarded.68:41
Unfair challenge on Chico by Louis Saha results in a free kick. Chico restarts play with the free kick.66:51 Substitution
Substitution Steven Fletcher goes off and Louis Saha comes on.65:48
Assist by Jonathan de Guzman.65:48 Goal scored
Goal! - Miguel Michu - Swansea 2 - 2 Sunderland Miguel Michu finds the back of the net with a headed goal from deep inside the penalty box. Swansea 2-2 Sunderland.
The ball is delivered by Jonathan de Guzman,63:26
Corner taken by Jonathan de Guzman from the left by-line, save by Simon Mignolet.63:12
Free kick awarded for a foul by Stephane Sessegnon on Nathan Dyer. Direct free kick taken by Jonathan de Guzman.62:29
The ball is swung over by Jonathan de Guzman, Miguel Michu has a header from deep inside the six-yard box and clears the crossbar.62:01
Inswinging corner taken from the left by-line by Jonathan de Guzman, save by Simon Mignolet.61:28
Unfair challenge on Jonathan de Guzman by James McClean results in a free kick. Angel Rangel takes the direct free kick.61:18
A cross is delivered by Angel Rangel, clearance made by David Meyler.56:55
Craig Gardner concedes a free kick for a foul on Danny Graham. Direct effort from the free kick comes in from Jonathan de Guzman, save by Simon Mignolet. Angel Rangel takes a shot. Carlos Cuellar gets a block in.55:26
Unfair challenge on David Meyler by Nathan Dyer results in a free kick. Simon Mignolet restarts play with the free kick.54:35
John O'Shea takes the free kick.54:35 Booking
Booking Caution for Ashley Williams.54:31
Steven Fletcher fouled by Ashley Williams, the ref awards a free kick.54:08
The ball is swung over by Angel Rangel, Jack Colback gets a block in. Angel Rangel produces a cross, John O'Shea manages to make a clearance.52:54
The ball is crossed by Angel Rangel, David Meyler makes a clearance.52:29
Nathan Dyer takes a shot. Simon Mignolet makes a save.50:23
Unfair challenge on Adam Johnson by Miguel Michu results in a free kick. The free kick is swung in left-footed by Adam Johnson, Ben Davies manages to make a clearance.48:47
Outswinging corner taken right-footed by Jonathan de Guzman, Shot from deep inside the area by Leon Britton goes over the bar.48:29
The ball is swung over by Angel Rangel, David Meyler manages to make a clearance.47:15
Centre by Ben Davies.45:51
Foul by Wayne Routledge on David Meyler, free kick awarded. Craig Gardner takes the free kick.45:01
The game restarts for the second half.45:00 +7:41 Half time
Half Time The half-time whistle blows.45:00 +6:24
The assist for the goal came from Sebastian Larsson.45:00 +6:24 Goal scored
Goal! - Steven Fletcher - Swansea 1 - 2 Sunderland Steven Fletcher scores a goal from close range low into the middle of the goal. Swansea 1-2 Sunderland.45:00 +5:53
Angel Rangel is penalised for handball and concedes a free kick. The ball is crossed by Sebastian Larsson,45:00 +4:16
The ball is delivered by Stephane Sessegnon, Angel Rangel makes a clearance.45:00 +2:42
The ball is swung over by Angel Rangel.45:00 +2:22
A cross is delivered by Adam Johnson, Chico makes a clearance.45:00 +1:39
Foul by Leon Britton on David Meyler, free kick awarded. Sebastian Larsson takes the free kick.45:00 +0:20
The assist for the goal came from Nathan Dyer.45:00 +0:20 Goal scored
Goal! - Wayne Routledge - Swansea 1 - 1 Sunderland Wayne Routledge finds the back of the net with a goal from close range high into the middle of the goal. Swansea 1-1 Sunderland.44:28
The ball is delivered by Nathan Dyer, Craig Gardner manages to make a clearance.42:51
The ball is crossed by Stephane Sessegnon, Strike by James McClean from inside the six-yard box clear the bar.41:44
Wayne Routledge delivers the ball.39:59 Goal scored
Goal! - Steven Fletcher - Swansea 0 - 1 Sunderland Steven Fletcher fires in a goal from deep inside the penalty box to the bottom left corner of the goal. Swansea 0-1 Sunderland.38:53
The ball is delivered by Ben Davies.37:43 Substitution
Substitution David Meyler joins the action as a substitute, replacing Lee Cattermole.37:24
Miguel Michu takes a shot. Blocked by John O'Shea.31:54
Wayne Routledge delivers the ball.31:30
Corner taken by Jonathan de Guzman from the right by-line, John O'Shea makes a clearance.31:13
Angel Rangel produces a cross, Craig Gardner manages to make a clearance.29:57
Free kick awarded for an unfair challenge on Wayne Routledge by Lee Cattermole. Ashley Williams restarts play with the free kick.29:23
Nathan Dyer gives away a free kick for an unfair challenge on Jack Colback. Direct free kick taken by Jack Colback.26:37
Angel Rangel crosses the ball, clearance by John O'Shea.23:01
The free kick is swung in right-footed by Jonathan de Guzman, save made by Simon Mignolet.23:01 Booking
Booking Craig Gardner receives a yellow card for unsporting behaviour.22:37
Free kick awarded for an unfair challenge on Wayne Routledge by Craig Gardner.21:54
Nathan Dyer takes a shot. Save by Simon Mignolet.21:05
Jonathan de Guzman takes a shot. Blocked by Carlos Cuellar.20:46
A cross is delivered by Ben Davies, clearance made by Carlos Cuellar.15:07
Adam Johnson crosses the ball from the free kick left-footed from right wing, save made by Michel Vorm.15:07 Substitution
Substitution Ben Davies comes on in place of Neil Taylor.15:07
Neil Taylor concedes a free kick for a foul on Craig Gardner.14:09
Neil Taylor challenges Adam Johnson unfairly and gives away a free kick. Craig Gardner takes the free kick.11:00
The ball is crossed by Angel Rangel, Simon Mignolet makes a comfortable save.9:40
Neil Taylor produces a left-footed shot from just outside the box that goes wide right of the goal.7:24
Nathan Dyer takes a shot. Simon Mignolet makes a comfortable save.6:46
Lee Cattermole fouled by Wayne Routledge, the ref awards a free kick. Free kick taken by Lee Cattermole.4:37
Neil Taylor delivers the ball, Craig Gardner makes a clearance.2:54
Simon Mignolet takes the free kick.1:57
Jonathan de Guzman crosses the ball, Carlos Cuellar makes a clearance.1:20
Corner taken by Jonathan de Guzman from the right by-line to the near post, clearance by Carlos Cuellar.0:35
Ashley Williams concedes a free kick for a foul on Steven Fletcher. Sebastian Larsson takes the direct free kick.0:00
The referee gets the game started.
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