Nacho Monreal and Gervinho's second-half goals secured a hard-fought win for Arsenal at Swansea to boost their Champions League qualification hopes.
Monreal scored his first Arsenal goal when he struck a low shot through a crowded penalty area into the bottom corner.
Substitute Gervinho sealed the victory in stoppage time with a sharp finish.
Michu had Swansea's best chance, as his team suffered their third home defeat of the season.
Manager Arsene Wenger had described the game at the Liberty Stadium as a must win in Arsenal's quest to finish in the top four.
But his side were rarely in danger, with Swansea not fully testing goalkeeper Lukasz Fabianski, who was making his first league start in more than two years.
Arsenal nearly had the perfect start when Alex Oxlade-Chamberlain's curled effort rattled the crossbar after he had cut inside Angel Rangel.
Full-back Rangel was then presented with an opportunity of his own when his advancing run was picked out by Ki Sung-Yueng.
But with only Fabianski to beat, Rangel's first touch let him down and he fired wide with the outside of his right foot.
Swansea v Arsenal 2012-13
Swansea won 2-0 at the Emirates in December but Arsenal beat the Swans in the FA Cup in January, winning 1-0 in the replay after the sides had drawn 2-2 at the Liberty Stadium.
Michu, scorer of three previous goals against Arsenal this season, was set up by Jonathan de Guzman after an error by Carl Jenkinson but his volley on the turn went narrowly wide.
After a flurry of Swansea activity, neat build-up play by the visitors resulted in a chance for Santi Cazorla, whose dipping volley forced Michel Vorm into his first save of the match.
Cazorla's chance was the start of a good spell for Arsenal but the Swansea defence held firm and Ashley Williams blocked Theo Walcott's goal-bound effort.
On the counter Michu continued to prove a danger and Fabianksi had to dive low to deny him, although the assistant referee had already flagged for offside.
With the rain lashing, Oxlade-Chamberlain again came close when his swerving shot from 25 yards clipped the top of the crossbar three minutes before the break.
This was the fourth meeting of the season between the sides and Swansea were looking to complete a league double over the Gunners having won 2-0 at Emirates Stadium in December.
But Arsenal started the second half brightly and Cazorla's shot from the edge of the penalty area was well gathered by Vorm.
Swansea were restricted to speculative efforts and Michu failed to trouble Fabianski with an effort that flew over the crossbar while compatriot Pablo Hernandez fired wide.
Arsenal stepped up the pressure and the deadlock was finally broken by January recruit Monreal.
The Spaniard pounced to lash a shot across Vorm into the bottom corner with the help of a deflection off Williams.
Gervinho wrapped up the victory after fellow substitute Aaron Ramsey's pass, firing low beyond Vorm and bringing Arsenal within two points of fourth-placed Chelsea.
Arsenal manager Arsene Wenger: "We will know at the end of the season how important this win is, but we knew as well the win was absolutely vital for us and we could not drop points today.
"We have shown we are up for the fight and we will do so until the end of the season. The attitude of the players was outstanding, even when our legs were less than fresh after playing in midweek.
"We kept going and refused to drop points. The players knew what was expected."
Swansea City manager Michael Laudrup: "I think in the first half we saw some good football from both sides.
"Our philosophies are similar and they had a couple of chances with Chamberlain hitting the bar, we had some good chances too.
"In the second half there was less good football. There was a lot of play in midfield but no shots on target.
"I thought it would be 0-0, but when things are like that the first goal will decide the game and that is what happened, it was a strange goal, but it was a goal and that decided the game."
- 01 Vorm
- 06 Williams
- 16 Monk
- 22 Rangel
- 33 Davies
- 07 Britton
- 09 Michu
- 11 Pablo
- 12 Dyer (Moore - 76' )
- 20 De Guzman Booked
- 24 Ki Sung-Yeung (Routledge - 66' )
- 25 Tremmel
- 02 Bartley
- 21 Tiendalli
- 15 Routledge
- 14 Lamah
- 17 Shechter
- 19 Moore
- 21 Fabianski
- 04 Mertesacker
- 06 Koscielny
- 17 Monreal
- 25 Jenkinson
- 02 Diaby (Ramsey - 71' )
- 08 Arteta Booked
- 14 Walcott (Gibbs - 85' )
- 15 Oxlade-Chamberlain (Gervinho - 71' )
- 19 Cazorla
- 12 Giroud
- 01 Szczesny
- 05 Vermaelen
- 28 Gibbs
- 07 Rosicky
- 16 Ramsey
- 22 Coquelin
- 27 Gervinho
Live Text Commentary
Full Time The referee signals the end of the game.90:00 +2:49
Carl Jenkinson delivers the ball, clearance by Ashley Williams.90:00 +1:17
Aaron Ramsey challenges Leon Britton unfairly and gives away a free kick. Leon Britton restarts play with the free kick.90:00 +0:11
Aaron Ramsey provided the assist for the goal.90:00 +0:11 Goal scored
Goal! - Yao Gervinho - Swansea 0 - 2 Arsenal Yao Gervinho gets on the score sheet with a goal from inside the box low into the middle of the goal. Swansea 0-2 Arsenal.88:02
Santi Cazorla takes a shot. Blocked by Garry Monk. Inswinging corner taken right-footed by Santi Cazorla from the left by-line.85:13
Free kick awarded for an unfair challenge on Jonathan de Guzman by Santi Cazorla. Angel Rangel takes the free kick.84:18 Substitution
Substitution Kieran Gibbs is brought on as a substitute for Theo Walcott.83:28
Santi Cazorla takes a shot. Ashley Williams gets a block in.82:06
Jonathan de Guzman shoots direct from the free kick.82:06 Booking
Booking Mikel Arteta is booked.81:55
Pablo Hernandez fouled by Mikel Arteta, the ref awards a free kick.79:50
Unfair challenge on Miguel Michu by Aaron Ramsey results in a free kick. Direct free kick taken by Leon Britton.78:23
Theo Walcott is ruled offside. Indirect free kick taken by Garry Monk.78:01
Theo Walcott takes a shot. Ashley Williams gets a block in.77:29
A cross is delivered by Ben Davies, Carl Jenkinson makes a clearance. Inswinging corner taken by Jonathan de Guzman from the left by-line.76:37
Yao Gervinho takes a shot. Save by Michel Vorm.75:23 Substitution
Substitution Nathan Dyer goes off and Luke Moore comes on.73:31
Olivier Giroud provided the assist for the goal.73:31 Goal scored
Goal! - Nacho Monreal - Swansea 0 - 1 Arsenal A goal is scored by Nacho Monreal from inside the penalty box to the bottom right corner of the goal. Swansea 0-1 Arsenal.
Outswinging corner taken from the right by-line by Theo Walcott.70:04 Substitution
Substitution Aaron Ramsey comes on in place of Vassiriki Diaby.70:04 Substitution
Substitution Yao Gervinho on for Alex Oxlade-Chamberlain.65:35 Substitution
Substitution Wayne Routledge joins the action as a substitute, replacing Sung-Yeung Ki.64:26
Free kick awarded for an unfair challenge on Theo Walcott by Ben Davies. Lukasz Fabianski takes the free kick.62:40
Angel Rangel is penalised for a handball. Mikel Arteta takes the direct free kick.61:23
The ball is crossed by Ben Davies, Carl Jenkinson gets a block in.60:44
The offside flag is raised against Angel Rangel. Free kick taken by Lukasz Fabianski.59:36
Jonathan de Guzman produces a cross, Pablo Hernandez takes a shot. Carl Jenkinson gets a block in. Corner from the left by-line taken by Jonathan de Guzman, Per Mertesacker manages to make a clearance.58:20
Pablo Hernandez has an effort at goal from outside the area which goes wide right of the goal.56:31
Shot from just outside the box by Miguel Michu goes over the bar.53:50
Santi Cazorla challenges Jonathan de Guzman unfairly and gives away a free kick. Angel Rangel takes the free kick.52:17
The ball is crossed by Carl Jenkinson, Pablo Hernandez gets a block in. Corner from the right by-line taken by Santi Cazorla, Michel Vorm makes a save.51:26
Santi Cazorla takes a shot. Save by Michel Vorm.50:23
The ball is crossed by Nacho Monreal, Angel Rangel gets a block in.49:16
Sung-Yeung Ki takes a shot. Blocked by Laurent Koscielny.48:02
Corner taken by Santi Cazorla, Ashley Williams makes a clearance.47:16
The ball is delivered by Carl Jenkinson, Ashley Williams makes a clearance.45:42
Shot by Vassiriki Diaby from outside the area goes high over the crossbar.45:01
The referee starts the second half.45:00 +3:37 Half time
Half Time The ref blows to end the first period.45:00 +0:56
Ben Davies produces a cross, clearance by Per Mertesacker. Corner taken right-footed by Jonathan de Guzman from the right by-line, clearance made by Laurent Koscielny.43:16
Nathan Dyer fouled by Nacho Monreal, the ref awards a free kick. Free kick taken by Angel Rangel, Jonathan de Guzman delivers the ball, clearance made by Per Mertesacker.42:29
The referee blows for offside. Per Mertesacker takes the free kick.41:21
Alex Oxlade-Chamberlain takes a shot.37:37
Alex Oxlade-Chamberlain takes a shot. Garry Monk gets a block in. Carl Jenkinson is penalised for a handball. Michel Vorm takes the direct free kick.37:26
Centre by Nacho Monreal, Garry Monk makes a clearance.35:34
The ball is swung over by Alex Oxlade-Chamberlain, Ben Davies gets a block in. Corner taken right-footed by Santi Cazorla, Sung-Yeung Ki makes a clearance.34:44
Theo Walcott takes a shot. Ashley Williams gets a block in. Corner taken by Santi Cazorla from the left by-line played to the near post, Sung-Yeung Ki makes a clearance.32:36
Miguel Michu is flagged offside by the assistant referee. Indirect free kick taken by Per Mertesacker.31:01
Carl Jenkinson sends in a cross.25:13
Theo Walcott produces a strike on goal direct from the free kick.25:13 Booking
Booking Jonathan de Guzman booked for unsporting behaviour.25:10
Jonathan de Guzman gives away a free kick for an unfair challenge on Santi Cazorla.22:00
Free kick awarded for a foul by Vassiriki Diaby on Jonathan de Guzman. Direct free kick taken by Leon Britton.18:30
Santi Cazorla takes a shot. Save made by Michel Vorm.16:21
Effort from the edge of the box by Miguel Michu goes wide of the right-hand upright.14:03
Effort from the edge of the area by Miguel Michu goes wide of the right-hand post.12:48
Angel Rangel has an effort at goal from just inside the box that misses to the right of the target.4:28
Alex Oxlade-Chamberlain takes a shot.3:13
Nathan Dyer produces a right-footed shot from just outside the box that goes wide right of the goal.1:33
The ball is crossed by Carl Jenkinson, blocked by Ben Davies. Outswinging corner taken right-footed by Santi Cazorla from the right by-line, Headed effort from deep inside the area by Olivier Giroud misses to the left of the goal.0:00
The game gets underway.
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