Tottenham is in 5th place with 57 points. Aston Villa are just above with two more points. 4th place will guarantee a place in the Champions League next season.
After just four minutes, Brennan Johnson put the visitors in the lead when he poked the ball into the goal from close range.
A quarter of an hour later, Kurt Zouma headed a corner from Jarrod Bowen into the back of the net.
Michail Antonio had a golden opportunity alone with Tottenham goalkeeper Guglielmo Vicario with half an hour left in the match, but the Italian goalkeeper stopped the attempt with a good save.
West Ham visit Wolverhampton in the next round, while Nottingham Forest.
Also read: Son secured Tottenham’s victory late in a hard-fought match