Alex Pritchard gave Spurs the lead after just six minutes with a sublime set-piece finish from range.
It was Pritchard who did the damage again on the half-hour, latching onto a clever pass from Milos Veljkovic to rifle home and give Spurs a two-goal advantage going into the break.
Spurs had chances to make the game safe early in the second half but some wasteful finishing prevented the home side kept the match alive.
Wolfsburg were handed a lifeline when Philip Hauck was fouled in the area by Jack Barthram. Hauck stepped up to reduce the deficit with a firmly-struck penalty.
A dramatic comeback was completed in stoppage time when Philipp Mueller rounded Luke McGee to break Spurs' resistance and earn the German visitors a valuable point.
The late fightback leaves Spurs and Wolfsburg level on four points in a group also containing Barcelona and Anderlecht.