Bayern beat Manchester United as Real Madrid, Arsenal win in Champions League
The meeting between German champions Bayern and a struggling United side, a repeat of the 1999 final, was the biggest game of the opening round of matches in this season's competition and it did not disappoint.
Leroy Sane gave Bayern the lead at the Allianz Arena with a shot that squirmed through the grasp of United goalkeeper Andre Onana, and Jamal Musiala set up Serge Gnabry to make it 2-0 just after the half-hour mark.
Rasmus Hojlund pulled one back early in the second half with his first United goal, but shortly after Christian Eriksen was penalised for a handball in the box and Kane blasted in the resulting penalty.
Sane hit the post for the hosts before a crazy finish saw Casemiro reduce the deficit again, substitute Mathys Tel score Bayern's fourth, and Casemiro nod in another at the death to make it 4-3.
"A crazy finish," Kane told British broadcaster TNT Sports after netting his fifth goal in six games for his new club.
"We lost a bit of concentration there in the last five minutes. Thankfully we were able to hold onto the lead.
"Overall it's a really good start to the campaign against a tough side."
Erik ten Hag's United team have now suffered three consecutive defeats in all competitions and lost four of their last five matches.
"After my mistake we lost control of the game. It's a difficult situation for us, for me," said Onana in reference to Bayern's first goal.
Thomas Tuchel's side are already in control of Group A, in which the other game saw Galatasaray come from two goals down to draw 2-2 with FC Copenhagen.
Goals from Mohamed Elyounoussi and Diogo Goncalves had the visitors in control in Istanbul but they then had Elias Jelert sent off and Galatasaray struck twice in the last four minutes of regulation