Son Heung-min's late winner fired Tottenham to a 2-1 win over Luton but Aston Villa beat Wolves 2-0 to retake fourth place in the Premier League from Spurs on Saturday.
Chelsea remain in the bottom half of the table after they twice blew a lead at home to 10-man Burnley in a 2-2 draw.
Spurs have now come from behind to win in four of their last five home games and needed another second-half turnaround to keep their challenge for a return to the Champions League next season on track.
Tahith Chong's strike after just three minutes gave Luton a shock lead, but the Hatters ended the day in the relegation zone as their winless run extended to 10 games.
An Ange Postecoglou half-time substitution again made an impact for Tottenham as Brennan Johnson's cross was turned into his own net by Issa Kabore just six minutes after the Welsh international's introduction.
Son had missed a number of chances earlier in the game but finally got some fortune when his deflected effort trickled past Thomas Kaminski for his 15th goal of the season.
"Until the end I was getting frustrated but I wanted to stay calm as captain," said Son.
"We don't want it to always end like this, it could be nicer when we have it (won) earlier."
Tottenham's victory briefly took them into fourth, but Villa responded as goals from Moussa Diaby and Ezri Konsa gave them the bragging rights from a Midlands derby.
Manchester United are now 12 points adrift of the top four ahead of their trip to Brentford later on Saturday.
Chelsea boss Mauricio Pochettino was met with another backlash at Stamford Bridge after his side failed to make the most of an extra man for the entire second half against second-bottom Burnley.
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