Tottenham were outplayed in the first half but were a different proposition after the interval with Kane pouncing in the 64th minute to score his 185th Premier League goal.
No other player has scored more Premier League goals for a single club, with England skipper Kane moving clear of Sergio Aguero's tally for Manchester City.
"It's been a fantastic nine or 10 years in the Premier League. Hopefully many more years to go. I always love scoring," said Kane.
"The most important thing is winning games. Credit to the boys, they dug deep. We need to start games better. We need to improve. But the sign of a good team is winning when you don't play at your best.
"Credit to Wolves, they made it difficult. In the second half we came out with intensity. We created chances and pressed better. We deserved the goal. We didn’t create too many chances after that but neither did they."
Wolves, who are now winless in their last 10 Premier League games, had 12 goal attempts to Tottenham's one in the first half but were unable to make their superiority count.
Tottenham then found some extra gears to seize control, with Kane and Son Heung-min both being denied by the woodwork before Kane headed in from a corner flicked on by Ivan Perisic.
It was Tottenham's 1,000th Premier League goal at home and lifted them to seven points from their opening three games, a point more than champions Manchester City, who play on Sunday, and Arsenal who are in action later on Saturday.