Second-half goals from Gifton Noel-Williams and Andrew Gray saw Burnley end a three-game winless run against 10-man Leeds.
The game came to life when Hayden Foxe was sent off on 52 minutes for handball - his second booking.
The Clarets took advantage of the extra man to go ahead when Noel-Williams fired home from the edge of the area.
Gray made it 2-0 with a neat finish from 12 yards and the home side held on despite David Healy's fierce late shot.
Burnley manager Steve Cotterill:
"There are a lot of sendings-off at the minute.
"We are a competitive side. After 16 games we had 18 yellow cards but we've had six sendings-off.
"The assessors need to ease up on the referees because we don't have enough players on the pitch. For the good of football the brakes need to be put on."
Leeds manager Dennis Wise:
"There was nothing between the sides, we competed well, we knew we would frustrate them and we did frustrate them.
"The lads worked very hard and believed they could get something out of it even at 2-0 down.
"I think the sending-off was the difference between the two teams."
Burnley: Coyne, Duff, Thomas, McGreal, Harley, Elliott (Mahon 86), James O'Connor, Hyde (McCann 62), Jones, Gray (Lafferty 89), Noel-Williams.
Subs Not Used: Jensen, Foster.
Goals: Noel-Williams 67, Gray 69.
Leeds: Stack, Foxe, Heath, Ehiogu, Crainey, Douglas, Derry, Westlake, Lewis (Healy 72), Moore (Horsfield 72), Blake (Kandol 55).
Subs Not Used: Warner, Carole.
Sent Off: Foxe (52).
Booked: Foxe, Westlake.
Goals: Healy 87.
Ref: P Dowd (Staffordshire).