- Dani Olmo (3', 44', 68' Pen)
England captain Kane had signed a four-year deal amid a media frenzy only hours earlier and made a substitute appearance in the second half but could not prevent a season-opening defeat against the German Cup winners.
Instead it was RB Leipzig's Dani Olmo who stole the spotlight with a hat trick to give Leipzig a first Super Cup triumph.
The hosts' performance left Bayern coach Thomas Tuchel fuming, saying it was as if the team had done no work in their four-week preseason.
"It is a big problem because it feels as if we had done nothing in the past four weeks," Tuchel said.
"I cannot explain it. It was just not enough in every department. I have just no idea why. There is no relation between our form and attitude going into the game and our performance on the pitch.
"It is not good. It is the worse thing because there is such a big discrepancy."
Spaniard Olmo pounced on Bayern's sloppy defending in the third minute to slot in for the lead and he added another with a superb flick and turn that left two defenders standing a minute before the break.
Leipzig's Mohamed Simakan had almost gifted Bayern an equaliser a little earlier, hitting the post in his effort to clear the ball.
With Bayern wasteful up front, squandering half a dozen chances, coach Thomas Tuchel brought on Kane, whose transfer cost a Bundesliga record €100 million ($110m), in the 64th minute to huge cheers from Bayern fans.
But he hardly got a look-in, with only three touches, and it was Olmo who scored again, this time with a penalty only four minutes later, to secure the first title of the season for his team.
"It was amazing night. We worked a lot over 90 minutes, also with possession," Olmo said. "I think it was a perfect game.
"We expected to win, we wanted to lift this trophy, and there is no better way to start the season," he said.
"We want to be up there. We have a competitive team."
Bayern, who kick off their Bundesliga season on Friday against Werder Bremen, will be hoping the addition of Kane will dramatically improve their conversion rate in attack this season, a problem they have been struggling with since the departure of Robert Lewandowski last year.
Information from Reuters was used in this report.
- Bastian Dankert