Goals from Anton Stach, Noah Okafor and Dominic Calvert-Lewin took Daniel Farke’s side nine points clear of the relegation zone with just four games remaining for those below them.
Leeds failed to reach a first FA Cup final since 1973 in a 1-0 defeat to Chelsea at Wembley last weekend.
But they are now up to 14th in an impressive first season back in the top flight to, along with Sunderland, buck the trend of promoted sides falling straight back to the second tier.
Burnley were only pipped to the Championship title by Leeds on goal difference last season.
But the Clarets have struggled much more with the step up as they have been relegated for the third time in as many seasons in the Premier League.
Burnley parted company with manager Scott Parker on Thursday despite his exceptional record of achieving promotion from the Championship with three different clubs.
The difference in what was at stake for both clubs was clear in the opening stages as Leeds burst out of the blocks.
Stach fired the home side in front after just eight minutes as Martin Dubravka got down slowly to the German’s low drive.
Leeds dominated the rest of the first half but had to wait for a two-goal burst in four minutes just after the break to seal the points.
A brilliant move was finished off by Okafor after Calvert-Lewin’s backheel picked out Jayden Bogle.
The Swiss forward has scored six goals in his last seven league games to see Leeds over the line in the relegation battle.
But it was Calvert-Lewin’s goals that kept his side afloat earlier in the campaign.
The England striker prodded home his 13th goal of the season from close range after Dubravka could only parry Ao Tanaka’s strike.
Burnley salvaged some pride from Mike Jackson’s first match in interim charge when Loum Tchaouna blasted in a late consolation. (AFP)
