Crossing the Welsh border has not been a productive passage for the Clarets in their recent history and so it proved again as Ki Sung-Yueng’s late goal made it another point-less trip to the Principality.
The Clarets have not won in Wales since 2000 and Ki’s first goal of the season extended that wait to end the run to 16 games.
More pertinently, the Welsh hoodoo extended the Clarets’ current winless streak in the Premier League into double figures as Swansea continued their escape from relegation danger inspired by Carlos Calvalhal.
The former Sheffield Wednesday manager has now overseen just one defeat in seven league matches and completing a hat-trick of home league wins lifted the Swans further away from the bottom three.
The Clarets remain comfortably positioned at the other end of the table but their frustrating wait for a win goes on.
Burnley had little to worry about for the best part of an hour as they defended solidly and more than matched one of the form teams of the division in creating the better of the few chances on offer.
But Sean Dyche’s men couldn’t force a break-through as they lacked any real penetration from a low-key performance and as Swansea wound things up for a late push, Ki’s skidding strike was enough to decide it and keep the Liberty Stadium’s feel-goof factor intact.
The return to starting duty of Matt Lowton in place of the injured Phil Bardsley was, not surprisingly, the only change for the Clarets following their successful fightback against Manchester City a week ago with Stephen Ward the only one of the injured posse to return via the bench.
And Burnley picked up where they left off against the league leaders with Johann Berg Gudmundsson, the scorer of the Clarets’ late leveller against City, creating an early chance for Jeff Hendrick which he drove against defender Alfie Mawson.
The Clarets comfortably had the better of the opening 25 minutes with the combination of Ashley Barnes and Sam Vokes causing Swansea problems as the Burnley front pair took turns to tee up a shooting chance for their colleague, Vokes going closest with an effort on the turn that flew just wide from outside the penalty area.
Swansea, re-vitalised since the appointment of Calvalhal at the turn of the year, were content to sit deep and try and play on the counter-attack through the pace of Nathan Dyer and running power of Jordan Ayew.
But the Clarets gave them few sights of goal in the opening half as they determinedly defended their box and the best chance to break the deadlock again came at the other end when Gudmundsson skied a hurried effort over the bar after Aaron Lennon’s cross had reached him beyond the far post.
Swansea – who put eight past Notts County in a mid-week FA Cup replay but remained the joint lowest scorers in the division – looked to up the tempo straight after the re-start.
But it was Burnley who threatened five minutes into the second half as Barnes curled another effort just wide and Gudmundsson was the next to try his luck as the Clarets kept knocking on the door, his well-struck drive forcing Lukasz Fabianski into the first save of the game as the Poland international touched the ball over the bar.
Swansea’s own lack of a cutting edge prompted Carvalhal into his first substitution with an hour gone as former Blackburn Rovers full-back Martin Olsson – booked in the first half for diving – was replaced by £18m January signing Andre Ayew.
Ayew’s return to the club brought a reunion with brother Jordan as the siblings were paired together for the first time since turning out for Marseille five years ago.
And the Swans’ added further to their attacking options with the introduction of Tammy Abraham with just under 20 minutes to go as the Clarets made a change at the same time, Scott Arfield replacing Lennon to help stiffen the visitors' resolve.
Nick Pope had been well protected by his back four – with Ben Mee and Kevin Long imposing in the middle of Burnley’s defence – but as Swansea turned up the pressure the Clarets’ keeper was tested for the first time.
Pope showed sharp reflexes to keep out an effort from Jordan Ayew as he deflected a Tom Carroll cross goalwards but with nine minutes to go, he was powerless to stop Ki pouncing for the winner and handing the Clarets a fourth away defeat of the campaign.
Kyle Naughton tried to work a shooting chance on the edge of the penalty area but instead he left the ball for the South Korean to strike a low shot through a crowd of bodies and into the bottom corner of the net to continue Burnley’s Welsh woes.
Burnley: Pope, Lowton, Long, Mee, Taylor, Gudmundsson (Nkoudou 86), Cork, Hendrick, Lennon (Arfield 74), Vokes (Wells 81), Barnes. Substitutes: Lindegaard, Westwood, Ward, O'Neill.
Swansea City: Fabianski, Naughton, van der Hoorn, Fernandez, Mawson, Olsson (A Ayew 59), Dyer (Abraham 74), Ki, Carroll, Clucas, J Ayew (King 90). Substitutes: Nordfeldt, Narsingh, Routledge, Bartley.
Booked: Olsson, A Ayew
Referee: Andre Marriner