The Spurs appeared to be in control of the game after Rodrigo Bentancur and Brennan Johnson scored goals to put them ahead 2-1 following Hee-Chan Hwang's early opener.
However, despite losing key man Matheus Cunha at half-time to injury, Wolves found a late leveller through Jorgen Strand Larsen, meaning they have taken seven points from Vítor Pereira's first three games in charge.
The draw means Spurs, who also missed a penalty through Heung-Min Son at 1-1 and were booed off at full-time, have failed to win in their last five home games and leaves them down in 11th in the Premier League table with only 24 points from 19 games.
It also leaves boss Ange Postecoglou under huge pressure.
TrendingA torrid month of December, with poor results matched by a growing injury list, had seen Spurs slip down the table, but they looked on track to finish 2024 with a win after a strong finish to the first half.
Postecoglou's depleted side could not add a third or hold on, though, and their injury curse struck again as Destiny Udogie limped off in the second half with a hamstring injury.