Tanguy Ndombele's strike after just 57 seconds gave Spurs a lead they looked determined to hold onto for the remaining 89 minutes.
The plan looked to be working until the 86th minute, when Pedro Neto's corner was glanced in by Romain Saiss.
After a disappointing performance against Burnley on Monday, Nuno Espirito Santo will be pleased with how his side bounced back to dominate one of the league's best teams.
Wolves dominate safety-first Spurs
Before, during and after the loss at Turf Moor, Nuno received a lot of criticism for being overly negative in his team selection, with Wolves struggling to create any chances of note apart from Fabio Silva's late penalty.
The story was completely different at Molineux. Wolves lined up in a 4-2-3-1 formation and reintroduced Silva and Adama Traore to the starting XI with the intention of getting at Spurs.
While their hand was perhaps forced by Jose Mourinho's extremely defensive tactics after Ndombele's opener, Wolves impressed after the first minute of play. Nuno's side had more shots, shots on target and possession than their visitors, and would have felt hard done by had they ended up with no points.
While this more expansive style of football has become synonymous with Wolves' performances against the top six, fans will hope Nuno employs a front foot system against the so-called 'lesser' Premier League sides.
Spurs' deadly duo kept quiet
With 20 Premier League goals between them in 15 games this season, it was obvious that Wolves would have to nullify the threat of Harry Kane and Son Heung-Min to get a positive result at Molineux.
The duo have set each other up for 12 league goals this campaign, but neither had a chance of note in Spurs' draw. Son, in particular, was feeding off scraps against Wolves' resolute defence and was replaced by Erik Lamela with ten minutes to go.
This bodes well for Wolves ahead of their trip to Old Trafford in less than 48 hours time, where they will face another in-form duo in Bruno Fernandes and Marcus Rashford.
Midfield struggles without box-to-box presence
With Leander Dendoncker injured and Owen Otasowie on the bench, Wolves were left with a midfield pairing of Ruben Neves and Joao Moutinho for the second time in two games.
The Portuguese duo were kept apart after performing poorly in the 4-0 defeat to West Ham in September, and while both are undeniably superb technical footballers, they are too similar to be able to operate as a partnership.
Just three minutes after Moutinho was withdrawn for Otasowie, Wolves clinched their equaliser and looked likely to net a winner.
The details of Dendoncker's injury have not been made public, but Wolves may need to invest in a powerhouse midfielder in January as the Belgian's absence leaves Wolves' midfield far too passive and predictable for opposing defences.