Bayern, who won the German Super Cup against Frankfurt last Sunday, looked far from ready for the Bundesliga season starting next week, failing to create chances against the regional club despite almost complete possession.
The Bavarians fielded a full-strength team but had to wait until Robert Lewandowski's close-range tap-in after 82 minutes to claim victory.
Their opponents, who had refused to move the fixture to one of the bigger stadiums in nearby Hamburg and the bigger revenues from more tickets saying such historic ties should be played on home turf, battled hard in front of the 7,500 crowd.
They even had as chance for a sensational lead late in the first half but unmarked Florian Nagel, who snuck into the box, saw his close-range effort blocked by Manuel Neuer.
They started running out of steam in the second half and Thiago Alcantara rattled the crossbar with a 20-metre shot. But just as Bayern got going their own fans interrupted the game for several minutes by throwing paper rolls onto the pitch.
Lewandowski, however, settled their nerves with his winner to send them through as new coach Niko Kovac breathed a sigh of relief.
Kovac's former club Frankfurt fared worse without him, suffering a 2-1 loss to Ulm to exit the competition but fellow Bundesliga clubs VfL Wolfsburg, Hoffenheim, Werder Bremen and Bayer Leverkusen advanced.
Borussia Dortmund are in action against Greuther Fuerth on Monday while last season's league runners-up Schalke 04 beat regional club Schweinfurt 2-0 on Friday.
(Reporting by Karolos Grohmann; Editing by Christian Radnedge)
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