Norwich extended their unbeaten run in the Premier League to nine games despite a spirited Swansea fightback.
A first-half strike from Steven Whittaker and headers from Sebastien Bassong and captain Grant Holt gave the visitors the advantage.
Second-half efforts from in-form forward Michu and Jonathan de Guzman put the Canaries under pressure.
A left-footed Robert Snodgrass free-kick made it four for the Canaries, before a late Michu consolation.
Canaries' good form
Swansea 3-4 Norwich
Norwich 2-1 Sunderland
Southampton 1-1 Norwich
Everton 1-1 Norwich
Norwich 1-0 Man Utd
Reading 0-0 Norwich
Norwich 1-0 Stoke
Norwich 2-1 Tottenham (League Cup}
Aston Villa 1-1 Norwich
Norwich 1-0 Arsenal
In chilly south Wales conditions the crowd at Liberty Stadium saw two sides brimming with confidence from the off.
Michael Laudrup's hosts entered into the fixture undefeated in their last six in the league and fresh from a 2-0 victory at Arsenal.
However, the visitors were in even better form - Norwich's eight games without a loss equalled their best run in the top flight back in October 1989.
That said, the Canaries had only scored five goals away from home all season before Saturday.
Both sides made two changes to their starting XI and Swansea recalled striker Danny Graham, who had scored six in his last four games against Norwich.
And it was the former Watford frontman who came closest for the Swans in the first half, a looping header cannoning off keeper Mark Bunn's crossbar after a De Guzman chip sent him clear inside the box.
Michu also came close, a deflected shot narrowly wide of Bunn's right-hand post with the keeper wrong footed.
In contrast, when Norwich created openings they converted them.
Laudrup: "It was not a very good performance."
First right-back Whittaker surged forward, exchanged passes on the flank with Snodgrass, then cut inside. The Scotland international travelled unchallenged into the Swansea area before unleashing a fierce drive past Gerhard Tremmel at his near post.
The Norwich lead was doubled 25 minutes later, Bassong leaping and connecting well with a hanging Grant Holt cross to bury his header home.
And it was Holt himself who claimed the third. A foul on the right flank allowed Snodgrass to curl in a free-kick. The Norwich captain eluded marker Ki Sung-Yeung and powered a header past the exposed Tremmel.
However, the visitors' three-goal advantage did not last long into the second half, Laudrup's men forcing an early corner after good work by Chico Flores on the right.
Michu's the main man
Swansea's Spanish frontman Michu is the top scorer in the Premier League with 12 goals, and they have come from only 20 shots on target.
The corner itself posed little threat, but it was collected out on the left by 19-year-old Wales international Ben Davies. His pass back to the onrushing Michu was inch- perfect, the Spanish striker burying his shot past Bunn.
Nine minutes later Swansea had a second and were back in contention. Nathan Dyer beat Javier Garrido on the right, and his ball in was not cleared. It fell to De Guzman on the edge of the area who converted his crisp volley with aplomb.
The hosts had the ball in the back of the Norwich net a third time, substitute Itay Shechter converting after Bunn spilled the ball under pressure from Michu. However, despite the public address system kicking into action, referee Howard Webb had blown for a foul on Bunn and play resumed.
The momentum was with Swansea, but the atmosphere was sucked out of Liberty Stadium with 15 minutes remaining. Swans captain Ashley Williams upended Holt 25 yards out and was cautioned. Snodgrass then stepped up and curled a sublime effort over the wall and in.
Hughton: "The first half was as good as we've been."
But Laudrup's team continued to chase, and in stoppage time they came close to stealing a point.
First De Guzman whipped in a tremendous cross that Michu headed in at the far post for his 13th of the campaign. Then a ball over the top was flicked on by Shechter, forcing Bunn to tip over his crossbar. That proved the final chance in a pulsating game, a result which ended Swansea's six games unbeaten and pushed Norwich up to 11th in the table.
Swansea City manager Michael Laudrup:
"In the first half we conceded three goals and it was not a very good performance. But the first half was as bad as the second was good. I think the players bounced back great. We scored two in 15 minutes and had a third one ruled out, which was a little harsh. But I don't think we deserved to win today after that first-half performance."
Chris Hughton, Norwich City boss:
"It wasn't easy, even when we got those goals in the first-half. Swansea are a wonderful footballing side, and it's obvious why they've had such a good start. We didn't do ourselves any favours conceding in that second half, but we showed great character to come back at them. I thought it was a fair result today, on the balance of play. We deserved it. Has this been overdue? Perhaps. We've been working hard for it."
Full Time The referee blows for the end of the match.
Chico produces a header from inside the area that goes over the crossbar.
Assist by Jonathan de Guzman.
90:00 +2:06 Goal scored
Goal! - Miguel Michu - Swansea 3 - 4 Norwich Miguel Michu grabs a headed goal from close in. Swansea 3-4 Norwich.
Corner taken right-footed by Jonathan de Guzman, Steve Morison manages to make a clearance.
90:00 +1:17 Substitution
Substitution Leon Barnett joins the action as a substitute, replacing Steven Whittaker.
Javier Garrido restarts play with the free kick.
Booking Angel Rangel receives a caution for unsporting behaviour.
Angel Rangel challenges Steve Morison unfairly and gives away a free kick.
Free kick awarded for a foul by Ben Davies on Robert Snodgrass. Free kick taken by Russell Martin.
Shot by Chico from outside the box goes high over the crossbar.
Itay Shechter takes a shot. Blocked by Sebastien Bassong.
Nathan Dyer takes a shot. Blocked by Sebastien Bassong.
Miguel Michu produces a left-footed shot from deep inside the penalty box which goes wide of the right-hand upright.
Substitution Steve Morison comes on in place of Grant Holt.
The ball is swung over by Javier Garrido, clearance by Sung-Yeung Ki.
Anthony Pilkington sends in a cross, Ben Davies manages to make a clearance. Short corner worked by Anthony Pilkington.
Nathan Dyer produces a right-footed shot from just outside the box that misses to the right of the target.
Jonathan de Guzman sends in a cross, clearance made by Bradley Johnson. Inswinging corner taken by Ben Davies from the right by-line, clearance by Steven Whittaker. Inswinging corner taken left-footed by Ben Davies, Steven Whittaker manages to make a clearance.
Assist by Grant Holt.
76:14 Goal scored
Goal! - Robert Snodgrass - Swansea 2 - 4 Norwich Robert Snodgrass hits the back of the net with a goal direct from the free kick from outside the penalty area to the bottom right corner of the goal. Swansea 2-4 Norwich.
Booking Ashley Williams is cautioned by the ref for unsporting behaviour.
Free kick awarded for an unfair challenge on Grant Holt by Ashley Williams.
Ben Davies delivers the ball, Miguel Michu produces a header from the edge of the box and misses to the right of the target.
Free kick awarded for an unfair challenge on Itay Shechter by Russell Martin. Miguel Michu takes the direct free kick.
Headed effort from inside the area by Miguel Michu misses to the left of the goal.
Free kick awarded for an unfair challenge on Chico by Grant Holt. Chico takes the direct free kick.
A cross is delivered by Jonathan de Guzman, clearance by Javier Garrido. Outswinging corner taken by Jonathan de Guzman, Ashley Williams takes a shot. Miguel Michu challenges Mark Bunn unfairly and gives away a free kick. Direct free kick taken by Mark Bunn. Mark Bunn makes a save.
Unfair challenge on Sung-Yeung Ki by Bradley Johnson results in a free kick. Free kick taken by Miguel Michu.
Substitution Danny Graham leaves the field to be replaced by Itay Shechter.
The ball is sent over by Anthony Pilkington.
Free kick awarded for an unfair challenge on Grant Holt by Chico. The ball is swung over by Javier Garrido, Grant Holt takes a shot. Save by Gerhard Tremmel.
The referee blows for offside against Angel Rangel. Free kick taken by Mark Bunn.
Corner from left by-line taken by Sung-Yeung Ki.
Miguel Michu takes a shot. Steven Whittaker gets a block in.
Assist by Nathan Dyer.
58:36 Goal scored
Goal! - Jonathan de Guzman - Swansea 2 - 3 Norwich Jonathan de Guzman grabs a goal from inside the penalty box to the bottom right corner of the goal. Swansea 2-3 Norwich.
Nathan Dyer produces a cross, Javier Garrido makes a clearance.
Unfair challenge on Grant Holt by Angel Rangel results in a free kick. Mark Bunn takes the direct free kick.
Ben Davies delivers the ball.
Danny Graham takes a shot. Save by Mark Bunn.
Foul by Wesley Hoolahan on Nathan Dyer, free kick awarded. The free kick is delivered right-footed by Jonathan de Guzman from right wing, save by Mark Bunn.
Foul by Bradley Johnson on Nathan Dyer, free kick awarded. Direct free kick taken by Chico.
The assist for the goal came from Ben Davies.
50:18 Goal scored
Goal! - Miguel Michu - Swansea 1 - 3 Norwich A goal is scored by Miguel Michu from the edge of the penalty box low into the middle of the goal. Swansea 1-3 Norwich.
Bradley Johnson takes the chance to get an effort at goal.
The ball is delivered by Angel Rangel, Javier Garrido gets a block in. Outswinging corner taken right-footed by Jonathan de Guzman from the right by-line, clearance made by Robert Snodgrass.
The second half kicks off.
45:00 +1:55 Half time
Half Time The first half comes to an end.
Shot comes in from Sung-Yeung Ki from the free kick, save by Mark Bunn.
Booking Booking for Russell Martin for unsporting behaviour.
Russell Martin challenges Miguel Michu unfairly and gives away a free kick.
Assist on the goal came from Robert Snodgrass.
43:04 Goal scored
Goal! - Grant Holt - Swansea 0 - 3 Norwich Grant Holt scores a headed goal from deep inside the penalty area. Swansea 0-3 Norwich.
Wayne Routledge gives away a free kick for an unfair challenge on Robert Snodgrass. Robert Snodgrass delivers the ball,
The referee blows for offside against Grant Holt. Ashley Williams takes the free kick.
Grant Holt provided the assist for the goal.
39:13 Goal scored
Goal! - Sebastien Bassong - Swansea 0 - 2 Norwich Sebastien Bassong finds the net with a headed goal from close in. Swansea 0-2 Norwich.
Wesley Hoolahan fouled by Chico, the ref awards a free kick. Free kick crossed left-footed by Robert Snodgrass from right channel, clearance by Chico.
Free kick awarded for an unfair challenge on Grant Holt by Jonathan de Guzman. Wesley Hoolahan restarts play with the free kick.
Miguel Michu takes a shot. Blocked by Jonathan de Guzman.
The referee gives a free kick against Anthony Pilkington for handball. Direct free kick taken by Chico.
Angel Rangel produces a cross, Headed effort from inside the area by Miguel Michu misses to the left of the goal.
Danny Graham takes a shot.
Shot from 18 yards by Robert Snodgrass. Save made by Gerhard Tremmel.
Sung-Yeung Ki concedes a free kick for a foul on Robert Snodgrass. The free kick is delivered left-footed by Robert Snodgrass from right channel, clearance by Angel Rangel.
Jonathan Howson challenges Sung-Yeung Ki unfairly and gives away a free kick. Shot comes in from Jonathan de Guzman from the free kick.
Free kick awarded for an unfair challenge on Nathan Dyer by Bradley Johnson. Chico takes the direct free kick.
Ben Davies concedes a free kick for a foul on Robert Snodgrass. Mark Bunn takes the direct free kick.
Ben Davies gives away a free kick for an unfair challenge on Grant Holt. Robert Snodgrass crosses the ball in from the free kick, Ben Davies makes a clearance.
Free kick awarded for an unfair challenge on Chico by Grant Holt. Ashley Williams takes the free kick.
The assist for the goal came from Robert Snodgrass.
15:09 Goal scored
Goal! - Steven Whittaker - Swansea 0 - 1 Norwich Steven Whittaker finds the net with a goal from the edge of the penalty box to the bottom right corner of the goal. Swansea 0-1 Norwich.
The ball is delivered by Anthony Pilkington, save by Gerhard Tremmel.
Robert Snodgrass takes a shot. Gerhard Tremmel makes a save.
Jonathan Howson takes a shot from just outaide the box and strikes the post.
Danny Graham produces a right-footed shot from just outside the box that goes wide right of the target.
Danny Graham has a headed effort at goal from deep inside the area missing to the left of the target.
Corner taken by Robert Snodgrass played to the near post, Bradley Johnson takes a shot. Save by Gerhard Tremmel.
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