Leeds endured another nerve-jangling finish but clung on to Matt Heath's first-half opener to boost their hopes of surviving relegation to League One. The hosts stormed out of the blocks and Heath outjumped the visitors' defence to power home a 21st-minute header from Alan Thompson's corner for the opener.
Frazer Richardson then saw his 35-yard volley clatter the crossbar but Leeds did not find the second they deserved.
However, other than Paul McVeigh's tame shot, Burnley did not create a chance.
Leeds manager Dennis Wise:
"We've pulled Hull closer and also now I think Leicester are two points in front of us as well. It's interesting.
"It's been down to the players. It would have been easy to go flat (after
defeat at Colchester), but they showed they were up for it, ready for it and
they're having a real bash at it.
"One thing I can say is I can't fault their commitment and character for what
they've done.
"It's taken us a long time to try to sort this situation out, a long time,
but we're gradually getting there. We'll have to wait and see."
Burnley manager Steve Cotterill:
"The second half we dominated. I don't think they got in our half hardly in the second half. "But that's probably going to happen, especially if they get their noses in
front they're not going to gamble too much at the end.
"But it was frustrating in the first half because we didn't do the things we
did in the second.
"We looked as if we'd had a few results and it was a sigh of relief for us in
the first period.
"But after half-time we were a lot better and played with more zip, a bit
more devilment, but not quite enough."
Leeds: Ankergren, Richardson, Michalik, Heath, Gray, Blake (Rui Marques 76), Kishishev, Thompson, Lewis, Healy (Armando Sa 90), Cresswell.
Subs Not Used: Stack, Johnson, Moore.
Goals: Heath 21.
Burnley: Jensen, Duff, Thomas, Caldwell, Harley, Elliott (Akinbiyi 69), James O'Connor (Spicer 74), Djemba-Djemba, Jones, McVeigh, Gray.
Subs Not Used: Coyne, Coughlan, McCann.
Booked: James O'Connor, Duff, Thomas.
Att: 23,528
Ref: S Tanner (Somerset).