Leeds eased fears they could be dragged into a relegation battle in their first season back in the Premier League for 16 years as Patrick Bamford's early penalty was enough to beat Burnley 1-0 on Sunday.
Marcelo Bielsa's men now enjoy a nine-point cushion over the drop zone as they moved up to 11th, but needed luck on their side as Burnley were controversially denied an equaliser by an error from the referee.
Leeds' thrilling 6-2 defeat at Manchester United last weekend saw Bielsa's commitment to attacking football, no matter the opponent, questioned.
And they needed a first clean sheet in five games to hold off a resurgent Burnley, who had boosted their own hopes of survival with a four-game unbeaten run prior to their visit to Elland Road.
The decisive moment in the game came after just five minutes when Bamford latched onto a long ball over the top and was wiped out by the onrushing Nick Pope.
Bamford fired home the resulting penalty into the top corner for his 10th goal of the season.
Burnley felt doubly aggrieved when Ashley Barnes smashed home after Illan Meslier fumbled a high ball into the box on 17 minutes.
The French goalkeeper was awarded a free-kick for backing in by Ben Mee and despite Meslier appearing to be the aggressor, the goal could not be reviewed by VAR as referee Robert Jones had blown for the foul before the ball hit the net.
Leeds could have extended their lead before the break but Bamford accidentally blocked a goalbound effort from Jack Harrison.
Burnley then enjoyed the better of the second half, but Meslier was rarely stretched other than a late drive from Barnes he turned behind at his near post.
Defeat leaves Sean Dyche's men still just two points above the bottom three in 16th.