Kane doubled Bayern’s advantage with a low right-footed strike past home goalkeeper Jiri Pavlenka from 15 yards.
Within four minutes, he had assisted the first of Leroy Sane’s two goals with a clever flick over the top.
Late on, Mathys Tel completed Thomas Tuchel’s side’s easy victory.
“I was a little nervous [and] excited to play the game,” Kane said after the game to broadcaster DAZN.
“We got off to a good start with a goal in the first few minutes.” There were a few butterflies, but instinct always takes over when I’m on the pitch.”
It was a good night for Bayern and the club’s record signing Kane, who arrived in Bavaria to much fanfare but had a terrible start in the German Super Cup, losing 3-0 to RB Leipzig.
Kane superbly laid on the first goal for Sane, billed as the man to eventually replace Robert Lewandowski’s boots over a year after the prolific Poland striker’s departure to Barcelona.
The former Manchester City winger raced clear to send a low effort into the bottom left corner thanks to his fast thinking.
After the break, Bremen attacked, but Kane scored the visitors’ second goal of the night, collecting Alphonso Davies’ exquisite ball before picking his position and firing low into the bottom left corner.
Bayern made many substitutions with Kane suffering from cramp.
Substitute Thomas Muller set up Sane’s second goal before Kane’s replacement, French teenager Tel, scored late.
Early indications of the Kane effect
Bayern has won the previous 11 Bundesliga titles, but their points total of 71 last season, which was just enough to beat a struggling Borussia Dortmund, was their lowest since finishing third in 2010-11.
They have attempted to make amends for that close call with many fresh acquisitions, including South Korean defender Kim Min-jae from Napoli.
Kane’s arrival has arguably captured the most attention and given the most reason for optimism that they will be able to maintain their domestic supremacy while competing for the Champions League once more.
Tuchel predicted before the game that the “Kane effect” would enhance his team’s “chances of winning massively,” and it’s simple to see why.
While England’s all-time leading scorer was not at his best, he nevertheless gave Bayern with a key focal point up front and interacted well with Sane, Kingsley Coman, and Jamal Musiala.
Despite failing to convert numerous earlier scoring chances, he proceeded to drop deep, find gaps between defenders, and finish unerringly when given with the ball by Davies.
