Kane had scored a hat-trick in their 7-0 demolition of VfL Bochum on Saturday but was left on the bench.
Bayern coach Thomas Tuchel, who was also missing three of his central defenders through injury, opted for 18-year-old Mathys Tel and Eric Maxim Choupo-Moting up front.
The pair combined perfectly with Tel whipping a cross into the box and Choupo-Moting drilling in to give Bayern the lead in the ninth minute.
Israeli keeper Daniel Peretz made his Bayern debut in goal but was rarely troubled in a one-sided encounter which was briefly interrupted after 30 minutes.
Bayern fans threw hundreds of tennis balls onto the pitch, in protest against the decision to hold the German Super Cup last month on the day of the Cup first round, forcing Bayern to delay their first round match.
It had no effect on their team's performance as they struck twice more in the first half to put the game to bed.
Konrad Laimer made it 2-0 with a looping header in the 40th and 20-year-old Frans Kraetzig volleyed in with the last kick of the first half.
France youth international Tel added a fourth from a tight angle in the 85th to continue his good form, having also scored three goals in the league so far this season.
