'Not perfect' Kane helps Bayern to win at Wolfsburg on Kompany debut
Jamal Musiala put Bayern 1-0 up after 19 minutes but Wolfsburg took the lead with two Lovro Majer goals in the first 10 minutes of the second half.
Bayern were nervy, with Ralph Hasenhuettl's side pouncing on several defensive errors.
A Kane header forced Wolfsburg's Jakub Kaminski into an own goal after 65 minutes and the England captain set up Bayern's third, laying on a pass for Serge Gnabry's 82nd-minute strike.
"It's not perfect yet", Kane told Bayern TV after the match, saying his side "got punished a little" in the second half.
"We're still obviously implementing some of the ideas of the coach.
"Obviously, the team is a lot stronger than this. I'm happy we've got a good week to work now, to get to work on the ideas the coach wants."
Bayern midfielder Joshua Kimmich echoed Kane's sentiments on network DAZN, saying "we lost control of the game due to many mistakes", adding they "reacted well" when they fell 2-1 behind.
With 20 minutes gone, Kane, starting his first match since the Euro 2024 final in Berlin, found Sacha Boey on the right flank.
The French defender dribbled past two Wolfsburg defenders and cut the ball across for Musiala, who tapped home to open the scoring.
Musiala has six goals in eight games against Wolfsburg, more than any other side.
Cool Majer
Wolfsburg were lucky to get away with what appeared to be a handball in the box 10 minutes later, with Kane shown a yellow card for remonstrating with the referee.
Bystanders in the first-half, Wolfsburg burst into life early in the second, grabbing the lead inside the first 10 minutes.
Boey, who was making just his second start for Bayern since joining in January, went from hero to villain just a minute after the break, bringing down Tiago Tomas in the box.
Majer coolly slotted home, sending Manuel Neuer the wrong way.
The Croatia midfielder hit the post with Neuer flatfooted just a minute later but did not need to wait long for another opportunity, his 55th-minute goal putting Wolfsburg in front.
Patrick Wimmer pressed Kim Min-jae into a mistake, collected possession and advanced on goal, drawing Neuer and laying off for Majer to score.
Kane was crucial in helping Bayern draw level after 65 minutes. The England captain headed a deflected Kimmich cross goalwards and the ball bounced in off Wolfsburg's Kaminski.
Kane created Bayern's winner with eight minutes remaining, finding Gnabry who booted home from close range.
Bundesliga winners in 2009, Wolfsburg have not beaten Bayern since 2015, a run of 21 matches.
In Sunday's later game, Heidenheim won 2-0 at promoted St Pauli thanks to second-half goals from Paul Wanner and Jan Schoeppner.
After 66 minutes and with St Pauli on the attack, Heidenheim broke, with Wanner finishing a length-of-the-field effort to open the scoring.
Schoeppner turned in a corner on the 82-minute mark to seal the result.
Heidenheim, who were promoted to the top division for the first time two seasons ago, have a 2-1 lead in their Europa Conference League tie with Swedish side Hacken, with the second leg to be played at home on Thursday.
Cult club St Pauli returned to the Bundesliga this season for the first time since 2011.
