Swansea claimed their first away win in the Premier League thanks to Nathan Dyer's swashbuckling performance.
Dyer pounced on Stephen Warnock's weak pass to give Swansea an early lead and continued to harass Aston Villa.
Wayne Routledge doubled Swansea's lead moments after half-time, following up to blast home the rebound when Danny Graham's shot came off the post.
Charles N'Zogbia almost grabbed a last-minute consolation but the Villa winger's shot cannoned off the bar.
The last time Swansea tasted victory away from home in the top flight was in 1982, when Robbie James's double saw the Welsh side win at Nottingham Forest.
A happy new year for Swansea - Rodgers
It took just four minutes for Swansea to open the scoring at Villa Park, though, as Dyer punished a terrible mistake by Warnock.
The winger pounced on a weak back-pass to Richard Dunne, intercepting the loose ball before charging forward and firing low across Bradley Guzan into the far corner.
Andrea Orlandi, making his first Premier League start, nearly doubled Swansea's lead soon afterwards as the Spaniard was allowed to advance on the Villa goal before whistling a left-foot shot just wide.
Villa were not lacking in threat themselves, with Gabriel Agbonlahor making hay on the right to help the home side force a series of corners.
But Swansea were still carving out the better chances and Dyer saw his cross-shot from wide on the right drift just over the junction of post and crossbar.
Villa's best opportunities continued to come via set pieces and from another corner James Collins rose highest, but his header lacked sufficient power to trouble Michel Vorm in the Swansea goal.
Wayne Routledge lets fly to double Swansea's lead at Aston Villa
Dyer continued to torment Villa, leaving Warnock sprawling in his wake before teeing up Graham - although his low shot was well saved by Guzan.
The Swansea chances continued to flow, this time Orlandi breaking into the box before cutting the ball back for Graham, only for the off-balance striker to spoon his shot across goal from eight yards out.
Whatever plans Alex McLeish may have hatched at half-time to improve Villa were in tatters within two minutes of the restart, as Routledge doubled Swansea's lead against his former club.
Graham hassled Guzan into a hurried clearance and Routledge picked up possession on the left before advancing and squaring to Graham, who had done well to get himself back onside.
McLeish understands Villa fans' frustrations
The striker should really have hit the target but instead his shot bounced invitingly off the post for Routledge to complete things, blasting low into the far corner for his first Premier League goal.
Villa did respond and it needed a good block to send Stephen Ireland's shot spiralling away from goal, while Dunne looped his header over the crossbar from the resulting corner.
Dyer had also not shirked his defensive duties and with 12 minutes remaining was given a deserved rest, with the no less potent Scott Sinclair replacing him.
While Villa were at last exerting some sustained pressure, Swansea stayed firm in the final third and remained dangerous on the counter.
Graham nearly sealed things at Villa Park, after Routledge sent the former Watford man away through the middle, and it needed a fine lunging tackle from Dunne to take the sting out of the Swansea striker's shot.
Guzan needed treatment after taking a boot to the face as he saved bravely at the feet of Joe Allen, who had come on for Orlandi early in the second half.
It took until the last minute of injury time for Villa to produce their only really threatening attack on the Swansea goal, but N'Zogbia's thunderous shot instead found the woodwork with Vorm beaten.
The long-awaited win on the road saw Swansea join Villa on 23 points, but claim 11th place just ahead of their hosts on goal difference.
Full Time The referee blows for the end of the match.
Charles N'Zogbia has an effort at goal from just inside the box that bounces off the post.
Stephen Warnock delivers the ball, clearance made by Angel Rangel.
90:00 +0:30 Booking
Booking Michel Vorm receives a yellow card for time wasting.
Darren Bent concedes a free kick for a foul on Steven Caulker. Michel Vorm takes the free kick.
Centre by Marc Albrighton, Darren Bent takes a shot. Save by Michel Vorm.
Corner taken by Alan Hutton played to the near post, Danny Graham manages to make a clearance.
A cross is delivered by Alan Hutton.
Substitution Barry Bannan on for Ciaran Clark.
Richard Dunne has a headed effort at goal from close in which goes wide right of the target.
Outswinging corner taken right-footed by Marc Albrighton, clearance by Steven Caulker.
A cross is delivered by Charles N'Zogbia, Neil Taylor makes a clearance.
Danny Graham takes a shot. Save made by Bradley Guzan.
Corner from the right by-line taken by Marc Albrighton, save by Michel Vorm.
Unfair challenge on Alan Hutton by Wayne Routledge results in a free kick. Direct free kick taken by Bradley Guzan.
Free kick taken by Bradley Guzan.
Substitution (Swansea) makes a substitution, with Scott Sinclair coming on for Nathan Dyer.
The referee blows for offside against Wayne Routledge.
Centre by Marc Albrighton, clearance made by Danny Graham.
Short corner taken by Marc Albrighton from the left by-line.
The ball is swung over by Marc Albrighton, clearance by Steven Caulker.
Marc Albrighton concedes a free kick for a foul on Joe Allen. Kemy Agustien takes the free kick.
Centre by Marc Albrighton, Ashley Williams makes a clearance.
Marc Albrighton crosses the ball, Leon Britton manages to make a clearance.
Free kick awarded for an unfair challenge on Kemy Agustien by Marc Albrighton. Steven Caulker restarts play with the free kick.
Substitution Stephen Ireland goes off and Marc Albrighton comes on.
Stephen Warnock sends in a cross.
Free kick awarded for an unfair challenge on Nathan Dyer by Ciaran Clark. Steven Caulker restarts play with the free kick.
Outswinging corner taken right-footed by Stephen Ireland from the right by-line, Header from deep inside the penalty area by Richard Dunne goes harmlessly over the crossbar. Nathan Dyer concedes a free kick for a foul on Stephen Warnock. Stephen Warnock delivers the ball from the free kick left-footed from left wing, clearance by Angel Rangel.
Effort from the edge of the box by Stephen Ireland goes wide of the left-hand post.
The ball is sent over by Charles N'Zogbia, clearance made by Kemy Agustien.
Corner taken left-footed by Charles N'Zogbia from the left by-line to the near post, Steven Caulker makes a clearance.
Corner from the left by-line taken by Charles N'Zogbia, Leon Britton makes a clearance.
Kemy Agustien takes the direct free kick.
Booking Richard Dunne is cautioned.
Foul by Richard Dunne on Nathan Dyer, free kick awarded.
Substitution Andrea Orlandi goes off and Joe Allen comes on.
Booking The referee books Andrea Orlandi for unsporting behaviour.
Corner taken left-footed by Charles N'Zogbia, Steven Caulker manages to make a clearance.
Gabriel Agbonlahor produces a cross.
Free kick taken by Stiliyan Petrov.
Substitution Alan Hutton joins the action as a substitute, replacing Carlos Cuellar.
Foul by Danny Graham on Stiliyan Petrov, free kick awarded.
Darren Bent gives away a free kick for an unfair challenge on Kemy Agustien. Ashley Williams takes the direct free kick.
Effort on goal by Ciaran Clark from deep inside the area goes harmlessly over the bar.
The assist for the goal came from Danny Graham.
46:37 Goal scored
Goal! - Wayne Routledge - A Villa 0 - 2 Swansea Goal scored by Wayne Routledge from close in to the bottom right corner of the goal. Aston Villa 0-2 Swansea.
Danny Graham takes a shot from close range that strikes the post.
The game restarts for the second half.
45:00 +2:07 Half time
Half Time The referee calls an end to the first half.
Charles N'Zogbia concedes a free kick for a foul on Andrea Orlandi. Kemy Agustien restarts play with the free kick.
The ball is swung over by Carlos Cuellar.
Charles N'Zogbia crosses the ball.
Centre by Stephen Ireland, clearance by Steven Caulker.
Steven Caulker takes the free kick.
Booking James Collins goes into the book.
Free kick awarded for an unfair challenge on Wayne Routledge by James Collins.
Corner taken left-footed by Charles N'Zogbia, clearance by Steven Caulker.
Effort on goal by Danny Graham from deep inside the penalty area misses to the right of the goal.
Free kick crossed by Stiliyan Petrov, Steven Caulker manages to make a clearance.
Booking Kemy Agustien booked.
Kemy Agustien challenges Stephen Ireland unfairly and gives away a free kick.
Unfair challenge on Gabriel Agbonlahor by Leon Britton results in a free kick. Charles N'Zogbia produces a shot on goal direct from the free kick.
The ball is crossed by Nathan Dyer, clearance made by Ciaran Clark.
Unfair challenge on Danny Graham by Richard Dunne results in a free kick. Free kick taken by Leon Britton.
Carlos Cuellar gives away a free kick for an unfair challenge on Wayne Routledge. Ashley Williams takes the free kick.
Nathan Dyer sends in a cross, Danny Graham takes a shot. Save by Bradley Guzan.
The ball is swung over by Angel Rangel, Richard Dunne manages to make a clearance.
Nathan Dyer crosses the ball, James Collins makes a clearance.
Richard Dunne sends in a cross, clearance by Ashley Williams.
Corner taken by Charles N'Zogbia from the left by-line, James Collins takes a shot. Save by Michel Vorm.
Corner taken right-footed by Stephen Ireland to the near post, clearance by Danny Graham.
Free kick crossed left-footed by Charles N'Zogbia, Ashley Williams makes a clearance.
Booking Steven Caulker receives a caution.
Steven Caulker challenges Stephen Warnock unfairly and gives away a free kick.
Gabriel Agbonlahor sends in a cross.
Nathan Dyer produces a right-footed shot from the edge of the area and misses to the left of the goal.
Stephen Ireland has an effort at goal from just inside the box that misses to the right of the goal.
Inswinging corner taken from the right by-line by Charles N'Zogbia. Inswinging corner taken by Charles N'Zogbia from the right by-line played to the near post.
Corner taken left-footed by Charles N'Zogbia from the right by-line, clearance made by Kemy Agustien.
Free kick awarded for an unfair challenge on Kemy Agustien by Darren Bent. Direct free kick taken by Ashley Williams.
Andrea Orlandi has an effort at goal from outside the penalty box missing to the wide right of the goal.
Charles N'Zogbia sends in a cross, Header by Gabriel Agbonlahor from deep inside the penalty area misses to the left of the target.
The ball is swung over by Carlos Cuellar.
4:00 Goal scored
Goal! - Nathan Dyer - A Villa 0 - 1 Swansea Nathan Dyer finds the back of the net with a goal from the edge of the penalty box to the bottom left corner of the goal. Aston Villa 0-1 Swansea.
The ball is delivered by Gabriel Agbonlahor, Angel Rangel manages to make a clearance.
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