An early goal from Scott Sinclair was enough to end the Clarets' unbeaten start to the season on an eventful afternoon in South Wales.
Sinclair struck after just eight minutes to decide a game which ended with both sides down to ten men after Darren Pratley and Burnley defender Tyrone Mears were dismissed within the space of two second-half minutes.
Both players received second yellow cards as the Clarets' one-man advantage lasted only a matter of moments.
Pratley sees red
And despite three attacking substitutions from boss Brian Laws, Burnley couldn't repair the early damage.
The Swans were full value for their lead as they carved out a succession of chances.
But despite living dangerously, the Clarets could still have taken a point if Chris Iwelumo had been able to extend his productive start to the season with Burnley's best chance of the game.
Burnley also piled on the pressure late on but with Iwelumo nursing an injury which must make him a doubt for international duty the visitors could not preserve their unbeaten record.
After making nine changes for the mid-week Carling Cup win at Morecambe, Laws had not surprisingly reverted to the starting line-up that beat Leicester a week previously.
Chris Iwelumo couldn't extend scoring run
But that side was soon on the rack as Swansea came flying out of the blocks once Ashley Williams had got away with an early error which almost let in Chris Iwelumo.
The Swans were lethal down their left wing where former Burnley loanee Nathan Dyer ran riot in the opening exchanges in tandem with over-lapping full-back Alan Tate.
And not surprisingly that was the source of the opening goal after just eight minutes as Tate got in behind the Clarets' defence from a Dyer pass to deliver a perfect cross along the six-yard line.
David Cotterill took a swing and a miss but behind him SINCLAIR was waiting to fire a shot into the roof of the net.
The Dyer-Tate combination had the Clarets constantly back-pedalling and Dyer provided chances for Stephen Dobbie and Cotterill which neither could convert.
Burnley were chasing shadows and with 23 minutes gone Dyer was at it again, threading in a pass for Darren Pratley to burst into the box and rattle the top of the bar with a rising shot.
Relief was rare for the Clarets, although around the half-hour mark a spell in possession almost led to an equaliser as Martin Paterson forced Dorus de Vries into a flying save as he aimed a curler towards the top corner.
And after Brian Jensen had kept his side in the hunt with a crucial save from Sinclair as he bore down on the Clarets' goal, Burnley should have been level by the break.
Ross Wallace had seen much of the play going past him the other way but when he got a chance to cross he provided the perfect ball for Iwelumo, who missed the chance to claim his third goal of the season when he headed badly wide.
That at least showed the Clarets remained a threat and twice more in the closing minutes of the half they had opportunities as Paterson waited unmarked to pounce as Wade Elliott was crowded out and Dean Marney then elected to shoot and dragged his effort just wide.
Brian Jensen kept the Clarets in the game
However, if Burnley thought that had signalled a turning of the tide at the start of the second half they were mistaken as Swansea poured forward again.
Pratley was booked for diving as he went down under a challenge from Andre Bikey in the penalty area before Jensen came to the Clarets' rescue again.
Sinclair again sprung the defence to run onto Cotterill's through-ball and it took a perfectly judged tackle by Jensen outside the box to stop the former Chelsea man scoring again.
The pace remained relentless and within the space of two minutes both sides found themselves down to ten men.
Pratley received his marching orders when a foul on Mears earned him a caution and within moments Mears was following the Swans' man down the tunnel when he caught Dyer and also went into referee Steve Tanner's book for a second time.
Laws sent on fresh legs in midfield in the shape of Jack Cork and also threw on Steven Thompson and Chris Eagles in a bid to force an equaliser.
And after Sinclair had almost caught out Andre Bikey at the other end, Thompson met a Danny Fox cross with a glancing header which almost surprised de Vries at his near post.
Eagles kept Burnley driving forward as Swansea began to defend with increased desperation in a fractious closing spell.
But a clear-cut chance just wouldn't come and with Iwelumo hampered by a hamstring injury, the nearest Burnley came to an equaliser was a snap-shot from Thompson which flew just wide and Wallace free-kick that dipped just over the bar in the fifth minute of injury time.
Burnley: Jensen, Mears, Fox, Carlisle, Bikey, Alexander (Cork 64), Marney (Eagles 72), Elliott, Iwelumo, Paterson (Thompson 68), Wallace. Substitutes: Edgar, Cort, Rodriguez, Grant.
Swansea: De Vries, Tate, Monk, Williams, Taylor, Gower, Cotterill (Allen 62), Pratley, Dyer (Orlandi 70), Dobbie (Kuqi 78), Sinclair. Substitutes: Lopez, Serran, Richards, Cornell.
Referee: Steve Tanner
Bookings: Mears 42, 60; Thompson 75, Cork 90 (Burnley)
Pratley 48, 58 De Vries 65, Taylor 90 (Swansea)
Sent off: Mears, Pratley