Goals from Stuart Dallas, Patrick Bamford and Rodrigo helped Marcelo Bielsa's side to their first league win over Spurs since November 2001.
Leeds were worthy winners, testing Hugo Lloris on a number of occasions throughout to put a big dent in Tottenham's hopes of a top-four finish.
The hosts deserved their lead at the interval. Dallas scored his eighth goal of the season - only Bamford has more for Leeds this term - when he hammered the ball into the roof of the net after Hugo Lloris was forced to palm away a miscued clearance from teammate Sergio Reguilon.
Spurs hit back against the run of play when Dele Alli's deflected pass found Son Heung-Min who expertly fired it pass Meslier. A clever run from Harry Kane had opened up a hole in the Leeds defence to give the South Korean the time and space to pick his spot.
Bamford regained the lead for United when Jack Harrison, whose deliveries from wide areas had caused Spurs plenty of problems, found Gjanni Alioski on his outside and the left-back got to the byline and cut it back for Bamford to finish expertly with England manager Gareth Southgate watching from the directors box.
Leeds had dominated the first half, enjoying 58 per cent of possession and producing four shots on target to Tottenham's one. Prior to kick-off, Leeds had failed to win at Elland Road against any of the nine sides above them in the Premier League table.
Lloris made two fine saves in the first 45 minutes when he got down low to turn Bamford's early effort behind for a corner and later on in the half he tipped Jack Harrison's shot over after the United midfielder had cut inside and aimed an excellent effort toward the top corner.
Spurs' only other big opportunity came when Harry Kane lifted the ball over Illan Meslier but the offside flag was raised as the ball nestled in the back of the net. VAR checked the incident with the decision proving incredibly tight on the video replay.
Leeds had won 12 of their league 14 games this season when taking the lead, including their last eight, but there were a few nervy moments as the visitors started to find more joy in the final third.
Kane had the ball in the net for a second time but the flag was raised with the England captain in a clear offside position.
Meslier then made two fine saves to thwart Serge Aurier and Erik Lamela while Kane had a free-kick which clipped the top of the crossbar.
Leeds had plenty of chances of their own as well. Some intricate football created the chance for Harrison but he fired over while Klich had an effort stopped by Lloris.
The win was sealed with five minutes from time when Raphinha broke down the left and squared to Rodrigo who finished emphatically past Lloris to round off fantastic display.
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