A sublime Leighton Baines free-kick set Everton on their way to a first away win in six attempts and ended Swansea's run of three consecutive victories.
Swansea dominated the first half but Baines struck after the break, finding the top corner from 25 yards.
Nikica Jelavic wasted two chances but the striker had a simple tap-in to deservedly extend Everton's lead.
Influential midfielder Steven Pienaar almost added a third as the home side capitulated after the break.
The result extended Everton's unbeaten record against the Swans to 15 games, and was a tactical victory for manager David Moyes.
He set out his team to pressure the home side high up the pitch, successfully cutting off the hosts' usual flow of possession from defence into midfield.
Everton, who join Manchester United and Norwich in winning at the Liberty Stadium this season, were effective rather than spectacular in the first half.
They had arrived with one eye on Tuesday's FA Cup replay against Sunderland, Moyes resting Johnny Heitinga, Marouane Fellaini and Roysten Drenthe.
Phil Jagielka was among those restored to the side and the centre-back proved a one-man wall in the first half as he repelled Swansea's best efforts.
His first telling intervention came on 24 minutes when he was at full stretch to cut out Gylfi Sigurdsson's low cross as Danny Graham waited for a tap-in.
Did you know?
- Everton scored twice in a Premier League game for just the second time in 18 matches
Joe Allen drove a 25-yard effort inches wide from the resulting corner.
He then slid in to block to Sigurdsson's shot before clearing Angel Rangel's dangerous delivery across the face of goal.
A wayward Jelavic header was Everton's only effort of note in the opening 45 minutes, but they gradually began to take control as the break approached.
The striker wasted a glorious opportunity early in the second half when he sliced high and wide after the ball fell to his feet inside the penalty area.
And then a 20-yard stinger from Darron Gibson brought Michel Vorm into action for the first time in the Swansea goal.
But the Dutch keeper had no chance just before the hour as Baines found the top corner to put the visitors ahead.
The left-back won the free-kick himself as he tempted Ashley Williams into a rash challenge 25 yards from goal in a central position. Vorm knew what was coming but Baines's execution was perfect.
Brendan Rodgers made a triple substitution as his side ran out of ideas, but a second Everton goal arrived within five minutes of the change.
Fellaini, on for Tim Cahill, outmuscled Williams near the by-line and his precise pass gave Jelavic a simple tap-in from inside the six-yard box.
Swansea were fortunate not concede again as Pienaar, whose influence grew as the game progressed, twice set up substitute Denis Stracqualursi.
- 01 Vorm
- 02 Williams
- 03 Taylor
- 04 Caulker
- 22 Rangel
- 07 Britton
- 11 Sinclair (McEachran - 72' )
- 15 Routledge (Lita - 71' )
- 24 Allen Booked
- 42 Sigurdsson
- 10 Graham (Moore - 71' )
- 25 Tremmel
- 05 Tate
- 16 Monk
- 17 McEachran
- 27 Gower
- 18 Lita
- 19 Moore
- 24 Howard
- 02 Hibbert
- 03 Baines
- 06 Jagielka
- 15 Distin
- 18 Neville
- 04 Gibson Booked (Heitinga - 84' )
- 17 Cahill (Fellaini - 58' )
- 21 Osman
- 22 Pienaar Booked
- 07 Jelavic (Stracqualursi - 81' )
- 01 Mucha
- 05 Heitinga
- 25 Fellaini
- 11 Stracqualursi
- 14 McFadden
- 19 Gueye
- 28 Anichebe
Live Text Commentary
Full Time The referee blows for the end of the match.90:00 +4:00
The ball is delivered by Neil Taylor, clearance made by Sylvain Distin.90:00 +3:37
Denis Stracqualursi gives away a free kick for an unfair challenge on Steven Caulker. Steven Caulker restarts play with the free kick.90:00 +2:12
Marouane Fellaini gives away a free kick for an unfair challenge on Gylfi Sigurdsson. Shot comes in from Gylfi Sigurdsson from the free kick.90:00 +1:01
Leon Osman decides to take the corner short.90:00 +0:40
Leon Osman takes a shot. Neil Taylor gets a block in.89:22
Drilled right-footed shot by Gylfi Sigurdsson. Sylvain Distin gets a block in.88:13
Foul by Johnny Heitinga on Neil Taylor, free kick awarded. Michel Vorm restarts play with the free kick.87:49
Centre by Steven Pienaar, Denis Stracqualursi takes a shot. Michel Vorm makes a save.86:35
A cross is delivered by Angel Rangel.85:50
Denis Stracqualursi is caught offside. Free kick taken by Steven Caulker.83:18
Michel Vorm takes the direct free kick.83:18 Substitution
Substitution Johnny Heitinga joins the action as a substitute, replacing Darron Gibson.83:18
Foul by Denis Stracqualursi on Neil Taylor, free kick awarded.83:07
Denis Stracqualursi takes a shot. Save by Michel Vorm.82:10 Booking
Booking The referee shows Steven Pienaar a yellow card for unsporting behaviour.81:55
Leroy Lita has an effort from just inside the box that misses to the left of the target.80:34
Free kick crossed right-footed by Gylfi Sigurdsson from right wing, save by Tim Howard.80:34 Substitution
Substitution Denis Stracqualursi on for Nikica Jelavic.80:34
Marouane Fellaini challenges Leon Britton unfairly and gives away a free kick.
The ball is sent over by Neil Taylor.78:25
Leon Osman handles the ball and concedes a free kick. Michel Vorm takes the free kick.77:08
Nikica Jelavic gives away a free kick for an unfair challenge on Leon Britton. Ashley Williams takes the direct free kick.75:26
Assist on the goal came from Marouane Fellaini.75:26 Goal scored
Goal! - Nikica Jelavic - Swansea 0 - 2 Everton Nikica Jelavic finds the back of the net with a goal from close in to the bottom left corner of the goal. Swansea 0-2 Everton.74:54
Centre by Leighton Baines, clearance made by Josh McEachran.74:21
Leon Osman fouled by Leroy Lita, the ref awards a free kick. Tony Hibbert takes the direct free kick.73:08
Nikica Jelavic has an effort at goal from close range which goes wide right of the goal.72:19
Free kick taken by Ashley Williams.72:19 Booking
Booking Darron Gibson receives a caution.72:08
Darron Gibson challenges Leroy Lita unfairly and gives away a free kick.71:41
Marouane Fellaini fouled by Ashley Williams, the ref awards a free kick. Darron Gibson restarts play with the free kick.71:03 Substitution
Substitution (Swansea) makes a substitution, with Josh McEachran coming on for Scott Sinclair.70:28 Substitution
Substitution Luke Moore on for Danny Graham.70:28 Substitution
Substitution Wayne Routledge leaves the field to be replaced by Leroy Lita.66:54
Gylfi Sigurdsson fouled by Phil Neville, the ref awards a free kick. Free kick taken by Ashley Williams.65:34
Outswinging corner taken right-footed by Leon Osman, Ashley Williams makes a clearance.63:31
The ball is crossed by Phil Jagielka, Neil Taylor manages to make a clearance.61:43
A cross is delivered by Neil Taylor, Phil Jagielka manages to make a clearance.60:19
Steven Pienaar has an effort at goal from just inside the box that misses to the right of the goal.58:20 Goal scored
Goal! - Leighton Baines - Swansea 0 - 1 Everton Leighton Baines grabs a brilliant goal direct from the free kick from just outside the penalty area to the top right corner of the goal. Swansea 0-1 Everton.56:56 Substitution
Substitution Marouane Fellaini replaces Tim Cahill.56:56
Ashley Williams challenges Leighton Baines unfairly and gives away a free kick.55:57
Shot from just outside the area by Scott Sinclair goes over the bar.55:27
Steven Pienaar has an effort at goal from just outside the box which goes wide of the left-hand post.53:56
Centre by Wayne Routledge, Header from deep inside the area by Danny Graham goes harmlessly over the crossbar.52:35
Darron Gibson produces a drilled left-footed shot from 25 yards. Save by Michel Vorm. Effort from inside the six-yard box by Nikica Jelavic goes wide right of the target.51:01
Centre by Angel Rangel, Tim Howard makes a comfortable save.47:28
Gylfi Sigurdsson takes a outswinging corner from the right by-line to the near post, clearance made by Nikica Jelavic.47:09
Effort on goal by Gylfi Sigurdsson from 25 yards. Sylvain Distin gets a block in.45:55
Shot from deep inside the area by Nikica Jelavic clears the crossbar.45:01
The second half kicks off.45:00 +1:41 Half time
Half Time The first half comes to an end.45:00 +0:55
Tim Howard takes the free kick.45:00 +0:55 Booking
Booking The referee shows Joe Allen a yellow card for unsporting behaviour.45:00 +0:50
Free kick awarded for an unfair challenge on Phil Neville by Joe Allen.45:00 +0:08
Angel Rangel crosses the ball, Phil Jagielka makes a clearance.43:44
The ball is sent over by Nikica Jelavic.43:13
A cross is delivered by Leighton Baines, clearance made by Steven Caulker.42:23
The ball is crossed by Nikica Jelavic, Ashley Williams makes a clearance.41:50
Phil Jagielka sends in a cross.39:46
Leighton Baines takes a inswinging corner from the right by-line to the near post, clearance made by Danny Graham.39:28
Leighton Baines takes a shot. Blocked by Leon Britton.39:21
Phil Neville crosses the ball.39:14
Leon Osman delivers the ball.38:18
The ball is swung over by Tony Hibbert, clearance by Joe Allen.38:10
The ball is crossed by Leighton Baines.37:38
Foul by Scott Sinclair on Tony Hibbert, free kick awarded. Darron Gibson restarts play with the free kick.36:10
Darron Gibson produces a right-footed shot from just outside the area that goes harmlessly over the target.35:11
Unfair challenge on Leighton Baines by Wayne Routledge results in a free kick. The free kick is swung in left-footed by Leighton Baines, clearance by Ashley Williams.33:24
Unfair challenge on Steven Pienaar by Angel Rangel results in a free kick. Free kick taken by Leighton Baines.32:56
The official flags Scott Sinclair offside. Phil Jagielka takes the indirect free kick.32:07
Steven Pienaar has an effort at goal. Blocked by Angel Rangel.30:45
Gylfi Sigurdsson takes the outswinging corner, clearance by Nikica Jelavic.27:43
Unfair challenge on Phil Neville by Gylfi Sigurdsson results in a free kick. Tim Howard takes the direct free kick.26:05
Gylfi Sigurdsson concedes a free kick for a foul on Phil Neville. Centre by Leighton Baines, Header by Nikica Jelavic from deep inside the penalty area misses to the left of the target.25:46
Steven Pienaar sends in a cross, Steven Caulker manages to make a clearance.24:12
Joe Allen has an effort at goal from outside the penalty box missing to the wide right of the target.23:58
Gylfi Sigurdsson takes a outswinging corner from the right by-line to the near post, Nikica Jelavic makes a clearance.23:32
The ball is delivered by Gylfi Sigurdsson, Phil Jagielka makes a clearance.22:59
The ball is sent over by Wayne Routledge.21:28
Neil Taylor produces a cross, Shot on goal by Wayne Routledge from just inside the area clears the crossbar.18:20
The ball is crossed by Scott Sinclair, Leighton Baines manages to make a clearance.15:26
Shot from just outside the area by Gylfi Sigurdsson misses to the left of the target.15:14
A cross is delivered by Wayne Routledge, clearance made by Sylvain Distin.15:08
Angel Rangel sends in a cross, clearance made by Phil Jagielka.12:50
Phil Jagielka challenges Scott Sinclair unfairly and gives away a free kick. Leon Britton takes the direct free kick.10:36
A cross is delivered by Tony Hibbert.9:04
Neil Taylor sends in a cross.8:55
Wayne Routledge sends in a cross.7:07
Centre by Leon Osman, save by Michel Vorm.5:59
Danny Graham takes a shot. Save by Tim Howard.4:31
Free kick awarded for an unfair challenge on Leon Britton by Tim Cahill. Ashley Williams restarts play with the free kick.2:53
Tim Cahill crosses the ball, clearance by Steven Caulker.0:45
Free kick awarded for an unfair challenge on Steven Pienaar by Angel Rangel. Tim Howard restarts play with the free kick.0:00
The referee gets the game started.
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