The hosts took a deserved lead when Toby Alderweireld put the ball in his own net on the ninth minute mark.
The Belgium defender redeemed himself when he brilliantly smashed the ball home to restore parity with less than 30 minutes left before the break.
Spurs went ahead on the cusp of halftime through Heung-Min Son, who was the quickest to the rebound after his penalty was saved by Pepe Reina.
Seven minutes after the break, a corner from Jack Grealish was met with a thunderous header from Bjorn Engles to bring the game level.
The game looked to be heading for a stalemate before a horrendous Engels error gifted Son the opportunity to snatch the maximum points for Jose Mourinho’s men, which he took.
In an interview with BBC Sports after the game, Mourinho admitted that although the visitors deserved to win, Dean Smith’s men did not deserve to lose.
"I thought we deserved to win but I think they did not deserve to lose. Villa played to win,” the former Chelsea and Manchester United boss said.
The win against the Villans has taken Tottenham into fifth and to within one point of Chelsea, who play Manchester United at Stamford Bridge on Monday.
