Leeds came from two down at half time to claim all three points with a superb second half performance.
Leeds made two changes from the side that beat Crystal Palace last weekend, Neil Collins and Paul Connolly replacing Andy Hughes and Andy O`Brien.
Max Gradel had an early chance for Leeds but shot wide of the target.
Jay Rodriguez had the home sides first effort but he also failed to trouble the target.
Gradel should have done better when he fired over when a ball into an unmarked Luciano Becchio might have been a better option.
Schmeichel made a good save to his left to keep out Iwelumo and force the ball out..
From the resulting corner Brian Easton was on hand to score after Bikey`s effort had been saved on the line.
Neil Collins should have brought Leeds level when he failed to hit the target with a free header.
Burnley doubled the lead when Jay Rodriguez got on the end of a long clearance before slotting past Schmeichel.
The home side were enjoying plenty of the game and Cork fired over the bar.
Leeds went in two down at half time and a first defeat in eight games looked on the cards.
Leeds made the perfect start to the second half when Becchio headed to Gradel who fired the visitors back into the game.
Burnley should have restored their two goal advantage soon after but Chris Iwelumo headed wide from a great position.
Simon Grayson made his first change of the afternoon when Ross McCormack replaced Neil Kilkenny.
McCormack was quickly involved but his weak shot was easily saved.
Leeds were level half way through the second half after excellent work between Connolly and Gradel down the right.
Connolly eventually found Becchio and the inform striker fired Leeds level.
Bradley Johnson missed a great chance minutes later to fire Leeds ahead when he fired wide of the target ahead surging into the Burnley area.
Leeds were now firmly in the ascendancy and Snodgrass was next to go close when his effort hit the bar after a tremendous run.
Snodgrass caused problems again minutes later when his cross was nearly turned into his own net by Bikey, who was relieved to see it cleared off the line.
The pressure that Leeds had enjoyed in the second half paid off with just five minutes remaining when Howson finished in style from distance after picking up the ball just inside the Burnley half.
Burnley had a great chance to equalise when they were awarded a free kick on the edge of the area but Bikey fired high and handsome.
Leeds should have wrapped the game up when Howson again had a great chance but Grant denied him.
With the fourth official showing five minutes of added time Thompson twice went close to equalising for the home side as Leeds started to look nervous.
Schmeichel then had to be on his toes to turn around a Guidetti effort.
The referee blew his whistle to the delight of the 4,000 travelling Leeds fans after a fantastic second half performance.
Grant, Mears, Carlisle, Bikey, Easton, Elliott, Marney, Cork, Wallace (Guidetti 78), Rodriguez, Iwelumo (Thompson 72)
Subs not used
Jensen, Duff, Harvey, Alexander, Edgar
Schmeichel, Connolly, Bruce, Collins, McCartney, Johnson, Kilkenny (McCormack 64), Snodgrass, Howson, Gradel, Becchio (Faye 90)
Subs not used
Higgs, Hughes,Somma, Paynter
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