United's win put on hold the title celebrations of champions-elect Manchester City.
Oliver Giroud's first-half header was cancelled out shortly after the break by Anwar El Ghazi as Villa held Chelsea 1-1.
The win moves Leeds up to third on 10 points, albeit having played an extra game, two points behind Villa, while leaders Everton, who have 13 points, are at Southampton on Sunday.
Gareth Bale's first appearance for Tottenham Hotspur for seven years, following his loan move from Real Madrid, was eclipsed by West Ham United who scored three times late on to draw 3-3 in the London derby.
Champions Liverpool were ripped apart 7-2 at Aston Villa and Manchester United were routed 6-1 at home by Tottenham Hotspur.
Watford and Bournemouth were relegated along with bottom club Norwich City, while Aston Villa survived thanks to a 1-1 draw at West Ham United.
United kept up their impressive chase for a top-four spot with a comfortable 3-0 win at relegation-threatened Villa.
British media had reported West Midlands Police opened an investigation after the midfielder was pictured leaving an estate in Birmingham following a traffic accident in March.
Son Heung-min struck a stoppage-time winner after a dreadful error from Bjorn Engels as Tottenham Hotspur won 3-2 at Aston Villa to move up to fifth in the Premier League.
The Argentine striker struck the third, fifth and sixth goals as City ran riot at Villa Park, taking his league tally to 177