Andre Ayew struck the winner three minutes from time as the Swans came from behind at Villa Park to earn their first away win of the season.
After a goalless first half, Aston Villa took the lead when Jordan Ayew headed home but Gylfi Sigurdsson hauled the visitors level with a superb 25-yard free-kick.
Swansea finished the game strongly, however, and grabbed all three points as Kyle Naughton's low cross was rifled home by Andre Ayew as he scored his fifth goal in ten games.
It saw the Swans move onto 13 points after ten games.
The Swans made three changes to the starting XI that lost at home to Stoke.
Kyle Naughton returned at right-back in place of Angel Rangel, while Ki Sung-Yueng and Gylfi Sigurdsson were back in midfield with Jack Cork and Modou Barrow making way.
Former Aston Villa winger Wayne Routledge, meanwhile, again missed out with a calf problem.
Villa welcomed striker Gabby Agbonlahor back into the side after he recovered from injury, while Jordan Ayew linesdup against his brother Andre as they joined the list of siblings to have faced each other in the Premier League.
Brad Guzan, Micah Richards (capt), Leo Bacuna, Idrissa Gueye, Gabby Agbonlahor (Adama Traore, 85), Kieran Richardson, Jordan Ayew, Alan Hutton, Joleon Lescott, Rudy Gestede, Jack Grealish (Carles Gil, 74).
Mark Bunn, Jordan Amavi, Ashley Westwood, Carlos Sanchez, Jose Crespo.
Lukasz Fabianski, Kyle Naughton, Federico Fernandez, Ashley Williams (capt), Neil Taylor, Ki Sung-Yueng, Jonjo Shelvey (Jack Cork, 85), Gylfi Sigurdsson, Jefferson Montero (Modou Barrow, 76), Andre Ayew, Bafetimbi Gomis (Eder, 90).
Kristoffer Nordfeldt, Angel Rangel, Kyle Bartley, Leon Britton.
Both sides came into this fixture looking for a change in fortunes, with Swansea without a win in five league matches and Villa not having tasted victory since the opening day of the season at Bournemouth.
And it was the hosts who had their first effort on goal after two minutes as Keiran Richardson’s free-kick was well held by Lukasz Fabianski.
But the Swans slowly grew into the game as Gylfi Sigurdsson flashed an effort wide after Villa had conceded possession, while Federico Fernandez blazed a volley over the crossbar following a well-worked corner routine.
However, with both teams searching for that elusive breakthrough, the contest became a scrappy affair with both Ashley Williams and Micah Richards picking up yellow cards for and off-the-ball incident.
Villa ended the half with two decent sights of goal, however, as Rudy Gestede shot wide of the left-hand post before the big striker rose highest to head over a corner from the right.
HALF-TIME:Aston Villa 0-0 Swans
Neither side made any changes at the break but it was Villa who nearly broke the deadlock two minutes after the restart as Gabriel Agbonlahor curled a shot a fraction wide of the left-hand post, before Leandro Bacuna flashed a low cross across the face of goal.
But the Swans responded with a good chance of their own just before the hour mark as Jonjo Shelvey sent Bafe Gomis clear of the Villa defence but the striker’s low strike was a couple of yards wide of goal.
The visitors then came even closer to opening the scoring as Gomis crossed into the box for Andre Ayew, but the Ghanaian’s powerful shot was superbly blocked by Brad Guzan.
However, that proved costly as Villa turned defence into attack to take the lead on 62 minutes.
Jack Grealish led the charge from midfield and after he found Agbonlahor on the edge of the box, then the striker crossed for Jordan Ayew to head home unmarked at the far post to the delight of the home crowd.
But the Swans roared back and were level five minutes later in spectacular fashion.
After Gylfi Sigurdsson was brought down 25 yards from goal, the Icelandic international stepped back up to curl home a sublime free-kick into the top corner.
Both sides made substitutions as Modou Barrow replaced Jefferson Montero for the visitors, while Grealish made way for Carles Gil for Villa.
And Barrow played a huge part as Swansea scored a crucial winner with just three minutes left on the clock.
The winger’s flick sent Kyle Naughton clear down the right flank and when the former Spurs man crossed low, Andre Ayew was there to slide the ball home from close range to send the travelling fans into raptures.