Teenager Tommy Wood got the only goal of the game as the Clarets' Development Squad secured a third successive 1-0 win.
Playing at Leeds' Thorp Arch training ground, Burnley were positive right from the start and when Josh Ginnelly dinked a nice ball over the defence for George Green to chase , the midfielder was denied by the home side's trialist goalkeeper.
It didn't take long for the Clarets to take the lead, though, as Arlen Birch played a neat pass down the right for the trialist playing right-back to square the ball into the area for youth-teamer Wood to poke the ball in from close range.
Michael Jolley's side came close again just 15 minutes in when Green's free-kick was met by the head of Birch who nodded just over the bar.
The Clarets were dominating and when Jamie Thomas found Robbie Leitch in the box, it looked as if the midfielder had doubled the lead only to be thwarted by an excellent save.
Leeds' first chance came just before the break when Mallik Wilks found space in the area but couldn't beat Clarets' keeper Connor Mitchell.
Burnley also started the second half on the front foot as they looked to double their lead and Leitch again went close with a deflected effort that went out for a corner.
United pushed for an equaliser as they threatened from set pieces with headers from Jack Vann and Matthew Downing both threatening the target.
But Burnley went closest to adding a second goal late on as Ginnelly was denied by a fine block.
Burnley: Mitchell, Trialist, Trialist, Dunne, Whitmore, Thomas, Leitch (Yao 57) Birch, Ginnelly, Green (Bayode 57) Wood (Koiki 57). Substitute: Aghayere.