The Clarets' winning run away from Turf Moor crashed to an agonising end as Leeds came from behind to pinch victory with a goal five minutes into stoppage time.
Burnley had played for more than an hour with ten men following the controversial dismissal of Kieran Trippier for two bookable offences and led when Charlie Austin scored a superb tenth goal of the season with just over 20 minutes to go.
But despite a heroic rearguard action, Eddie Howe's men found a fourth straight clean sheet and a fourth successive away win just beyond them as Leeds struck twice in the dying stages.
The Yorkshiremen had produced a similar fightback at Turf Moor in November to take the points but this was even more painful for the Clarets as they lost for only the second time in eight games.
It was the 87th-minute before Leeds managed to find a way past a never-say-die defence courtesy of a deflection off Jay Rodriguez and then with virtually the last kick of a gripping game, Ross McCormack punished a mistake by goalkeeper Lee Grant to leave Burnley with nothing to show for their gargantuan efforts.
Elland Road has rarely been a happy hunting ground for the Clarets, with only one win there in the past 37 years, although Burnley coudln't have asked for a better chance to take an early lead and build on a run that had propelled them onto the fringe of the play-off places.
Charlie Austin puts the Clarets in front
Austin, starting in place of Martin Paterson in his first game since being injured against Leeds seven weeks ago, was sent clear by Rodriguez's perfectly weighted pass.
But perhaps conscious of a closing Leeds defender, the striker lacked the composure to hit the target a he steered a right-footed effort wide with just three-and-a-half minutes gone.
The Clarets struggled for any real fluency but again went closest with Austin forcing Andy Lonergan to tip over his long-range effort in less than convincing fashion.
Leeds, looking to improve on a run of only one win in six homes games and avoid a fourth straight defeat, were far from nervy but couldn't make their possession count, even after the Clarets were reduced to ten men.
Controversy as Kieran Trippier sees red
Two cautions in the space of five minutes proved costly for Trippier, who was given no leeway by referee Mark Brown after twice impeding runs from Andros Townsend .
Despite what the Clarets later insisted was minimal contact and undeserving of a further booking, Trippier saw red following only his second foul of the afternoon to stack the odds against the visitors.
The dismissal prompted a rapid re-shuffle with Andre Amougou coming on in place of Junior Stanislas to fill the middle of the defence, with David Edgar moving sideways to plug the gap at right-back left by Trippier's departure.
With a man short, Austin was left to play a lone role in attack with the Clarets surrendering territory but not the lead as they set out their stall to frustrate the home side.
But if it was a barricade of yellow and claret thrown up before the break, Burnley's backs were forced even closer to the wall after the re-start as they were made to repel a wave of white shirts.
Frustration as Leeds make it 1-1.....
Only a magnificent clearing header from Ben Mee kept the damn intact before a looping header from Darren O'Dea hit the top of the bar as Leeds got ever closer.
Grant's flying save then kept out a free-kick from Ramon Nunez and Zac Thompson sent a skidding volley flashing inches wide as the Clarets cleared a corner.
And with their back line refusing to budge, Burnley then remarkably took the lead.
Austin had been forced to feed off scraps on the few occasions Howe's men got forward but when Chris McCann's header dropped for him 22 yards from goal, the fit-again frotnman swivelled and steered the perfect volley across Lonergan into the bottom corner to claim his first goal since the end of October.
That proved to be Austin's last contribution before making way for former Leeds loanee Sam Vokes as the Clarets battled to see out a famous win.
....and devastation as Leeds win it in injury time
It was nerve-shredding stuff and when Grant dropped a high ball into the box, substitute Mikael Forssell missed a great chance to level when he volleyed over the top.
But despite their heroics, the Clarets couldn't quite hold out as Leeds finally made the break-through with three minutes of normal time to go.
Burnley had kept out any number of corners but this time when Adam Clayton delivered the ball hard towards the near post, the cruellest of deflections off Rodriguez took the ball past Grant and into the back of the net.
In injury time Lloyd Sam then flashed a shot across the face of goal, possibly via the finger tips of Grant although no corner was given.
And the Clarets were within seconds of a treasured point when with virtually the last kick of the game, and the allotted five minutes played, McCormack pounced to break Burnley hearts after Grant, having stood firm for so long, spilled a shot from Townsend.
Brian Easton feels the pain
Leeds United: Leeds United: Lonergan, Bruce, O'Dea, Kisnorbo (Sam 17), White, Townsend, Clayton, Thompson, Pugh, Nunez (McCormack 74), Becchio (Forssell 70). Subs: Brown, McCarthy.
Booked: Pugh 45
Burnley: Grant, Trippier, Easton, Edgar, Mee, Marney, McCann, Wallace, Stanislas (Amougou 36), Rodriguez, Austin (Vokes 74). Subs: MacDonald, Hines, Stewart.
Booked: Trippier 23, 28, Edgar 53, Mee 62, Grant 90+3.
Sent off: Trippier
Referee: Mark Brown