Brennan Johnson gave Spurs the lead inside three minutes but that was largely where their attacking threat ended. Pablo Sarabia and Mario Lemina scored in the 91st and 98th minutes to succumb Spurs to a second defeat in five days.
Despite fielding a makeshift back four, Spurs took the lead in the third minute when Pedro Porro found 22-year-old Johnson for a tap-in. Spurs then held on to their slender lead for 90 minutes.
Wolves' Hwang Hee-Chan and Sasa Kalajdzic both had shots that went just wide, but it was substitute Sarabia who finally gave the home side an equaliser in the 91st minute when he expertly controlled a cross and volleyed home from an angle.
With a draw on the cards, Lemina then timed his run in the 97th minute perfectly to get on the end of a Sarabia pass to stroke the ball into the bottom corner for all three points.
The result leaves Spurs second in the table while Wolves move up to 12th.