UNITED 1 (Heath 21), BURNLEY 0
United: Ankergren, Richardson, Heath, Michalik, Gray, Blake (Marques 77), Kishishev, Thompson, Lewis, Healy (Sa 90), Cresswell. Subs: Stack, Johnson, Moore.
Burnley: Jensen, Duff, Thomas, Caldwell, Harley, Elliott (Akinbiyi 70), Djemba-Djemba, James, O'Connor (Spicer 74), Jones, McVeigh, Gray. Subs: Coyne, Coughlan, McCann.
Referee: Steve Tanner
Att: 23,528
David Healy pulled on the captain's armband for the first time for the crucial clash with Burnley at Elland Road as United looked to bounce back from Monday's defeat at Colchester.
Boss Dennis Wise made three changes from the side which lost at Layer Road with Frazer Richardson, Robbie Blake and Richard Cresswell all returning to the starting line-up in place of Rui Marques, the suspended Jonathan Douglas, and Tresor Kandol.
Having slipped back into the drop zone following Monday's defeat, a confidence-boosting start was needed against Burnley and, with just four minutes on the clock, the new skipper tested visiting keeper Brian Jensen with a low drive.
Healy was also on the case when Richard Cresswell fired in a low centre and Burnley defender Wayne Thomas had to react well to cut out the cross.
It was United who made most of the early running and the breakthrough came on 21 minutes when Alan Thompson whipped over a cross from the right and Matt Heath sent a header crashing past Jensen.
Three minutes later, Richardson almost doubled the advantage when he struck the bar with a terrific effort from distance.
Jensen then pulled off an acrobatic save to turn a Cresswell header over the bar, following a free-kick from Richardson.
United continued to enjoy the better of proceedings, and it wasn't until the 32nd minute that Burnley fashioned out an opening for Paul McVeigh, the loan man firing wide of the mark.
But it was United who again came close to scoring a second. In a replica of the first goal, Thompson whipped in another corner from the right, Heath again made a good connection, but Burnley keeper Jensen pulled off a vital save.
The visitors did create another opening moments before half-time when Eric Djemba-Djemba fed Thomas, but Casper Ankergren smothered the defender's shot at close range.
There was a controversial moment early in the second half when, after giving away free-kick on the edge of the box, Lubo Michalik was despatched to the touchline for blood wiping from a head-wound. Despite an immediate return, referee Steve Tanner refused to let Michalik resume until after the kick was taken.
Thankfully for United, who defended the set-piece with 10 men, McVeigh's delivery was poor and the ball drifted harmlessly across the face of goal.
United's first real opportunity of the half came on 62 minutes when Richardson drilled the ball into the box, but the low centre proved a yard too far for Eddie Lewis to make a connection.
Wise made his first change of the afternoon just four minutes from time when he introduced Rui Marques in place of Robbie Blake.
With 11 minutes remaining, United again came close to finding the killer second goal when Lewis headed a Healy cross against Burnley defender Thomas, but the ball fell kindly into the arms of Jensen.
As the final minutes ticked away it was tight and tense - a situation Elland Road fans have become used to in recent home games. The fourth official added on three minutes of stoppage time and Burnley pushed men forward but United held on for the victory.