Spurs invited pressure on themselves and conceded goals from Willy Boly, Raul Jimenez and Helder Costa in the space of 15 minutes to remain six points adrift of leaders Liverpool, who have a game in hand to play.
Wolves, the first side to take points off Tottenham at Wembley since October, move into seventh place with their eighth win of a memorable first campaign back in the top flight.
Going in search of a seventh successive win under the famous arch, Tottenham started well and came close through shots from Son Heung-min and Kieran Trippier, the latter testing Rui Patricio with his free kick from 25 yards.
It was from a similar range that Christian Eriksen was denied by Patricio from a fine fingertip stop 20 minutes in, shortly after the same player had curled one inches over the crossbar.
Patricio could not get enough to the ball to keep out Kane's shot from his weaker left boot, though, with the Englishman cutting in from out wide and guiding the ball into the far corner for his 157th goal in Tottenham colours.
Wolves, who had earlier had a penalty shout rejected when Adama Traore's cross hit Ben Davies on the arm, felt that the goal should have been ruled out because of a foul from Harry Winks in the build-up to Kane's strike.
Son nearly went one better than Kane with his attempt from further out before the first half was over, marginally missing the target as Spurs went through the motions.
The slow-tempo feel to the match continued into the opening stages of the second half, with the first notable piece of action arriving 25 minutes from time when Davinson Sanchez produced a good challenge to prevent Ivan Cavaleiro from racing in behind - a sign of things to come.
Matt Doherty miscued a shot when teed up 15 yards out and as Wolves took complete control of possession, and they were rewarded for their attacking play thanks to Boly's header.
Tottenham had failed to register a single shot between the start of the second half and Boly's leveller, and there was a further blow to come before full time.
Jimenez picked up possession on the edge of the box, squeezed the ball through Trippier's legs and into the bottom corner.
Wanderers' fourth away league win in 10 outings this term was sealed by Costa, who was slipped in behind by Doherty and tucked the ball past Lloris with a fine finish after Tottenham committed too many men forward.
Tottenham had a strong penalty shout rejected for a shove on Kane in added time, but ultimately it was their decision to sit back and protect their slender lead that cost them the chance to close the gap on Liverpool.
TOTTENHAM HOTSPUR (4-3-1-2): Lloris; Trippier, Alderweireld, Sanchez, Davies; Sissoko, Winks, Dele (Lucas 68'); Eriksen; Son, Kane
WOLVERHAMPTON WANDERERS (4-3-2-1): Patricio; Bennett, Coady, Boly; Doherty, Dendoncker (Moutinho 68'), Neves, Jonny; Cavaleiro (Gibbs-White 85'), Traore (Costa 59'); Jimenez