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.
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.
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.
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.