Kane lost his marker near the back post to head in following a flick-on from Ivan Perisic at a corner in the 64th minute.
It was his 185th Premier League goal, moving him into outright fourth place in the all-time top-flight list above former Manchester City striker Sergio Aguero. Only Alan Shearer, Wayne Rooney and Andrew Cole are above him.
Tottenham have seven points from a possible nine, having opened the season with a 4-1 win over Southampton.
Wolves, who only have one point from three games, started new signing Matheus Nunes in midfield and had the better of the first half to frustrate Spurs and the home fans.
The visitors didn't create any clear-cut chances, though, and Tottenham came more into the game after halftime as Perisic — making his first start since his move from Inter Milan — started to have some joy down the left.
Kane headed against the crossbar from a cross by Dejan Kulusevski and Son Heung-min was denied by a last-ditch tackle after being sent through by Kane's quick free kick.
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