The Whites were shell shocked at Old Trafford but an early penalty from Patrick Bamford edged out all three points against the Clarets.
Marcelo Bielsa’s team returned to form with a high energy start as Bamford put them ahead after five minutes.
Burnley keeper Nick Pope clattered into him inside the box and the former Chelsea man continued his impressive start to Premier League life and smashed home from the spot.
The hosts continued to dominate from there on as Rodrigo Moreno tested Pope and the England keeper produced an instinctive stop from Jack Harrison.
Sean Dyche’s side did haul themselves into it after the restart with Matt Lowton and Ashley Westwood testing Illan Meslier.
Leeds looked comfortable to bed in the closing stages and eek out the win but Dyche’s side missed a golden chance to nick a point.
Leeds completely failed to clear their lines as Westwood’s cross wormed its way to Jay Rodriguez, but the Burnley fans favourite could only lash over the bar.
Full Time at Elland Road it’s Leeds United 1 Burnley 0