Two goals inside eight second-half minutes condemned the Swans to a third away defeat of the season.
But despite yet another strong performance on the road - Stephen Dobbie put the Swans ahead at the break - the visitors conceded twice in the second period.
Bradley Johnson pulled Leeds level 10 minutes after the re-start while Luciano Becchio scored the winner soon afterwards.
The Swans felt they should have been awarded a penalty when substitute Joe Allen was wrestled to the ground but referee Grant Hegley waved play on.
stepped in to fill the vacancy left by suspended midfielder Darren Pratley
The former Barcelona youngster started his first league game since April in an otherwise unchanged Swansea City starting line-up.
Neil Taylor continued at left-back after making his full debut in the last outing against Burnley while David Cornell
and Joe Allen
, who only returned from Wales Under-21 duty on Wednesday, were on the bench.Leeds:
Shane Higgs; Paul Connolly, Neil Collins, Richard Naylor (C)
, Fede Bessone
; Max Gradel, Neil Kilkenny (Ross McCormack, 79'), Jonathan Howson, Bradley Johnson; Sanchez Watt (Lloyd Sam, 56'), Luciano Becchio (Davide Somma, 86').Not Used:
Jason Brown (GK), Alex Bruce, Adam Clayton, Andrew Hughes.Swans:Dorus de Vries
; Alan Tate
; Ashley Williams
, Garry Monk(C)
, Neil Taylor; Nathan Dyer
(Cedric van der Gun
, 79'), Mark Gower
, Andrea Orlandi
, 69'), Scott Sinclair; David Cotterill
; Stephen Dobbie
.Not Used:David Cornell
(GK), Jordi Lopez
, Albert Serran
, Casey Thomas
, Shefki Kuqi
Leeds is always going to be a difficult place to come and play with manager Brendan Rodgers even commenting beforehand that his side would be in for a "tough afternoon" at Elland Road.
But times have certainly changed since the Swans' last visit three years ago - they're now an established second tier club for starters, with that overawed feeling of coming away to a big club (hopefully) in the past.
This game, though, did see the home side start strongly with Max Gradel heading into the hands of Dorus de Vries
early on before Luciano Becchio seeing his eighth minute effort deflect wide for a corner.Nathan Dyer
had put a dangerous ball across goal just momens before, one that was too strong for both Stephen Dobbie
and Scott Sinclair to reach, but the winger did win his side a free-kick in dangerous territory on 10 minutes, only for David Cotterill
to see it easily collected by Shane Higgs.
But the Whites' stand-in 'keeper was helpless three minutes later as he was beaten by the game's first goal.David Cotterill
's long ball forward slipped past skipper Richard Naylor which allowed Stephen Dobbie
to charge down on goal, the Scotsman kept his cool as he neared goal and placed the ball across Higgs and into the far corner.
And one almost became two to cap off a dream start with just 18 minutes played, Sinclair beating the offside trap to latch on to Cotterill's through ball only to fire straight at the 'keeper.
Following a spell of Leeds pressure their goalkeeper came to the rescue again on the half-hour, this time denying Dyer from close-range with a move orchestrated by Alan Tate
, Cotterill and Dobbie.
There was no doubt that the visitors were on top with every successful pass met by cheers from the travelling Swans supporters.
And they were almost given another goal to celebrate 90 seconds before half-time when that man again, Higgs, was on form to tip a Stephen Dobbie
shot destined for the bottom corner around the post.
But it was Leeds who could have had the last laugh as Bradley Johnson was given acres of space to stride forward before clipping the top of the bar with a dipped shot in stoppage-time.Half-Time:
Leeds 0 Swans 1
Scott Sinclair had been a thorn in Leeds' side from the start and when referee Grant Hegley got the second-half underway he had made his way to the opposite left flank.
Pace, as we all know, is his asset and just six minutes in he left Paul Connolly standing as he cut inside and launched an unstoppable shot towards Shane Higgs, beating the 'keeper but not the post.
But Leeds managed to find a way back into this contest with 55 minutes played, Max Gradel's free-kick into the box met by Richard Naylor's head, forcing Dorus de Vries
into an excellent save, but Bradley Johnson was left with space to fire the follow-up beyond the Dutchman and into the net.
And within 10 minutes the Whites found themselves in front - again de Vries was forced into making two fine saves from substitute Lloyd Sam and Neil Kilkenny, but when it fell to the unmarked Luciano Becchio he made no mistake in making it 2-1.
The Swans needed a boost and with 20 minutes left Joe Allen
was sent on, and within two minutes he came close twice to forcing a leveller. The first as he attempted to latch on to Nathan Dyer
's through ball, which was cleared for a corner, before closely connecting with a Cotterill cross from the right.
And the Wales star had good cause to feel irate inside the final quarter of an hour as he was wrestled to the ground inside the area, making a good plea for a penalty, which came either side of two Stephen Dobbie
Dobbie had two further chances late on but the visitors failed to replicate their first-half showing as they went down to a third consecutive Championship defeat on the road.