Arsenal's worst start to a season under Arsene Wenger continued as Michu scored two late goals to leave Arsenal 10th in the Premier League table.
Spanish striker Michu struck with two minutes left, curling the ball home after a neat one-two with Luke Moore.
Nathan Dyer's persistence then sent Michu clear and another composed finish gave Wojciech Szczesny no hope.
Gervinho wasted Arsenal's best chance when he made a mess of a free header in front of goal.
The midweek draw at Everton had already given Arsene Wenger his lowest points tally at this stage of the season - 21 points from 14 games - since taking over at Arsenal 16 years ago.
The groans of discontent were loud and clear as his players trudged off after another toothless display that leaves them five points behind fourth-placed rivals Tottenham.
Arsenal improved considerably after a poor first half as they starved Swansea of possession, but Michu's double strike as the game began to peter out gave them no chance to recover.
His controlled left-footed finishes took his tally to 11 for the season, further emphasising the bargain price of £2m Swansea paid to take him from Rayo Vallecano in the summer.
Wenger had targeted this game - the first of four at home from the next six - as a springboard to climb up the table and back into the title race.
But those hopes now lie in tatters and it will be Swansea who will be looking upwards as they move to within three points of the top four.
"Swansea were superb in the first half; Arsenal better in the second but not good enough. And the difference between the two sides was Michu - two chances right at the end that he took with aplomb."
There were early warning signs for Arsenal as the visitors began playing with a confidence borne from manager Michael Laudrup's instruction to express themselves without the constraints of pressure.
Sharp, intricate passing released full-back Angel Rangel behind the static Arsenal back four, but Szczesny was alert to save his first effort and then block the second shot on the rebound.
The Gunners were then indebted to a last-ditch lunge from Thomas Vermaelen to deny Dyer, whose hesitation after running free from the halfway line gave the Arsenal captain a chance to recover.
Despite a lack of invention, pace and fluidity, Arsenal could easily have scored twice before half-time through Gervinho.
The striker was inches away from connecting with an inviting cross from Carl Jenkinson, but then got it all wrong when left unmarked six yards out.
So poor was Gervinho's attempt that Theo Walcott retrieved the ball before it went out for a throw-in.
The Gunners finally showed some urgency and appetite after the break, quickly forcing Gerhard Tremmel into a first save when Santi Cazorla delivered a low drive.
Two half-hearted penalty claims were then waved away before Szczesny continued his personal duel with Rangel to deny him with another fine save.
Gervinho's ineffectual afternoon ended just after the hour mark, and his replacement, Olivier Giroud, gave referee Mark Clattenburg a tight call to make almost immediately.
Giroud was brought down by a desperate Chico Flores lunge on the edge of the area, but Clattenburg saw the faintest of touches from the Swansea defender.
Arsenal continued to probe, and Swansea were fortunate that Vermaelen's far-post header went straight at Tremmel.
But having offered little after the break, the Swans struck with ruthless efficiency to snatch all three points.
A simple one-two was enough split the home defence to release Michu for the first, and his lifted side-foot finish beat the out-stretched hand of Szczesny.
Another incisive finish followed two minutes later after Jenkinson's attempted backpass was deflected into his path by the tenacious Dyer, leaving Swansea to celebrate only their second away win over the Gunners.
Arsenal manager Arsene Wenger: "We are in this job to turn things around, and I am confident we will [because of] the quality of the players and the spirit we have in the team.
"It is a good moment to stick together.
"I am not so much worried about [league] places, even if that is not the place you want to be, but I believe what is important is we get the quality of our game back. Then the places change."
Swansea City manager Michael Laudrup: "There have been three great performances, each better than the [previous] one.
"The team is playing with a lot of confidence. They [Arsenal] put us under pressure for 20 minutes in the second half and you know their players can make the difference at any moment, so you can never sit easy.
"We looked in quite good shape and were only defending deep a few times."
- 01 Szczesny
- 04 Mertesacker
- 05 Vermaelen Booked
- 25 Jenkinson
- 28 Gibbs
- 08 Arteta
- 10 Wilshere (Rosicky - 79' )
- 14 Walcott
- 19 Cazorla
- 09 Podolski (Giroud - 67' )
- 27 Gervinho (Oxlade-Chamberlain - 66' )
- 24 Mannone
- 18 Squillaci
- 07 Rosicky
- 15 Oxlade-Chamberlain
- 16 Ramsey
- 22 Coquelin
- 12 Giroud
- 25 Tremmel
- 04 Chico
- 06 Williams
- 22 Rangel
- 33 Davies
- 07 Britton
- 09 Michu
- 12 Dyer
- 20 De Guzman (Tiendalli - 74' )
- 24 Ki Sung-Yeung
- 17 Shechter (Moore - 67' )
- 13 Cornell
- 16 Monk
- 21 Tiendalli
- 26 Agustien
- 29 Richards
- 19 Moore
- 41 Donnelly
Live Text Commentary
Full Time The game is over, as the referee blows his whistle.90:00 +2:03
Free kick awarded for an unfair challenge on Chico by Alex Oxlade-Chamberlain. Gerhard Tremmel takes the free kick.90:00 +0:49
Nathan Dyer provided the assist for the goal.90:00 +0:49 Goal scored
Goal! - Miguel Michu - Arsenal 0 - 2 Swansea Miguel Michu fires in a goal from inside the penalty area low into the middle of the goal. Arsenal 0-2 Swansea.89:19
Corner taken by Theo Walcott played to the near post, Angel Rangel manages to make a clearance.87:20
Luke Moore provided the assist for the goal.87:20 Goal scored
Goal! - Miguel Michu - Arsenal 0 - 1 Swansea Miguel Michu scores a goal from deep inside the penalty box low into the middle of the goal. Arsenal 0-1 Swansea.85:48
Thomas Vermaelen takes a shot. Comfortable save by Gerhard Tremmel.85:31
Santi Cazorla takes a shot. Ashley Williams gets a block in.84:24 Booking
Booking Thomas Vermaelen is shown a yellow card for unsporting behaviour.84:16
Unfair challenge on Santi Cazorla by Dwight Tiendalli results in a free kick. Mikel Arteta takes the direct free kick.83:15
Ashley Williams concedes a free kick for a foul on Olivier Giroud. Free kick taken by Mikel Arteta.82:57
Dwight Tiendalli takes a shot. Wojciech Szczesny makes a comfortable save.80:41
Ashley Williams fouled by Tomas Rosicky, the ref awards a free kick. Direct free kick taken by Ashley Williams.79:57
Dwight Tiendalli challenges Alex Oxlade-Chamberlain unfairly and gives away a free kick. Free kick taken by Tomas Rosicky.78:37 Substitution
Substitution (Arsenal) makes a substitution, with Tomas Rosicky coming on for Jack Wilshere.77:45
The official flags Luke Moore offside. Thomas Vermaelen restarts play with the free kick.75:08
Luke Moore takes a shot. Per Mertesacker gets a block in. Outswinging corner taken right-footed by Sung-Yeung Ki from the right by-line to the near post. Free kick awarded for an unfair challenge on Mikel Arteta by Chico. Direct free kick taken by Wojciech Szczesny.73:48 Substitution
Substitution Dwight Tiendalli joins the action as a substitute, replacing Jonathan de Guzman.72:32
Miguel Michu takes a shot. Wojciech Szczesny makes a comfortable save.
Nathan Dyer concedes a free kick for a foul on Theo Walcott. Per Mertesacker takes the free kick.71:41
Santi Cazorla takes a shot. Comfortable save by Gerhard Tremmel.70:14
Mikel Arteta takes a shot. Blocked by Ben Davies.69:44
Corner from the left by-line taken by Theo Walcott, clearance by Ben Davies. Outswinging corner taken by Theo Walcott from the right by-line played to the near post, Sung-Yeung Ki makes a clearance.66:31 Substitution
Substitution Luke Moore on for Itay Shechter.65:57 Substitution
Substitution Olivier Giroud joins the action as a substitute, replacing Lukas Podolski.65:57 Substitution
Substitution Alex Oxlade-Chamberlain is brought on as a substitute for Yao Gervinho.65:46
Jonathan de Guzman produces a right-footed shot from just outside the area that goes harmlessly over the target.63:45
Carl Jenkinson concedes a free kick for a foul on Jonathan de Guzman. Direct free kick taken by Ben Davies.62:57
The assistant referee signals for offside against Miguel Michu. Wojciech Szczesny takes the free kick.61:41
Angel Rangel takes a shot. Save by Wojciech Szczesny. Inswinging corner taken right-footed by Jonathan de Guzman from the right by-line.59:51
Santi Cazorla takes a shot. Comfortable save by Gerhard Tremmel.59:24
Corner taken by Theo Walcott from the left by-line, save by Gerhard Tremmel.55:26
Inswinging corner taken by Theo Walcott from the left by-line played to the near post, Angel Rangel manages to make a clearance.53:54
Itay Shechter takes a shot. Per Mertesacker gets a block in. Inswinging corner taken by Jonathan de Guzman from the left by-line, clearance by Per Mertesacker. Free kick awarded for an unfair challenge on Kieran Gibbs by Ashley Williams. Wojciech Szczesny takes the direct free kick.49:00
Mikel Arteta concedes a free kick for a foul on Itay Shechter. Miguel Michu restarts play with the free kick.48:25
Outswinging corner taken from the right by-line by Theo Walcott.47:27
Santi Cazorla takes a shot. Comfortable save by Gerhard Tremmel.45:01
The match restarts for the second half.45:00 +0:07 Half time
Half Time The match has reached half-time.44:35
Headed effort on goal by Yao Gervinho from inside the penalty box misses to the right of the target.43:20
The assistant referee flags for offside against Itay Shechter. Direct free kick taken by Per Mertesacker.41:31
Free kick awarded for a foul by Jack Wilshere on Itay Shechter. Free kick taken by Miguel Michu.40:21
Santi Cazorla concedes a free kick for a foul on Miguel Michu. Ben Davies restarts play with the free kick.37:49
Unfair challenge on Leon Britton by Jack Wilshere results in a free kick. Free kick taken by Leon Britton.36:13
Unfair challenge on Miguel Michu by Mikel Arteta results in a free kick. Jonathan de Guzman fires a strike on goal direct from the free kick.30:07
Nathan Dyer takes a shot. Blocked by Thomas Vermaelen. Corner taken right-footed by Jonathan de Guzman, clearance made by Mikel Arteta.28:34
Sung-Yeung Ki gives away a free kick for an unfair challenge on Mikel Arteta. Jack Wilshere takes the direct free kick.28:11
Santi Cazorla takes a shot. Gerhard Tremmel makes a comfortable save.26:45
Itay Shechter is penalised for a handball. Per Mertesacker takes the direct free kick.26:30
Lukas Podolski takes a shot. Blocked by Chico.25:28
Free kick awarded for a foul by Angel Rangel on Yao Gervinho. Jack Wilshere takes the direct free kick.22:10
Itay Shechter is caught offside. Wojciech Szczesny takes the free kick.21:31
Unfair challenge on Nathan Dyer by Kieran Gibbs results in a free kick. Free kick crossed right-footed by Sung-Yeung Ki.20:22
Free kick awarded for a foul by Jack Wilshere on Jonathan de Guzman. Leon Britton takes the direct free kick.17:15
Corner taken by Theo Walcott played to the near post, Miguel Michu manages to make a clearance.13:43
Angel Rangel takes a shot. Save by Wojciech Szczesny. Angel Rangel takes a shot. Save by Wojciech Szczesny. Outswinging corner taken from the right by-line by Jonathan de Guzman, Per Mertesacker manages to make a clearance.12:19
The official flags Angel Rangel offside. Kieran Gibbs takes the free kick.10:12
Corner taken right-footed by Theo Walcott from the right by-line, save by Gerhard Tremmel.8:34
Effort from outside the penalty box by Carl Jenkinson goes wide left of the target.6:01
Itay Shechter is caught offside. Wojciech Szczesny restarts play with the free kick.4:25
Thomas Vermaelen challenges Miguel Michu unfairly and gives away a free kick. Free kick taken by Jonathan de Guzman.3:48
Jonathan de Guzman gives away a free kick for an unfair challenge on Jack Wilshere. Per Mertesacker takes the direct free kick.0:00
The match gets underway.
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