Bayern, last year's runners-up, named a strong side against the Bundesliga strugglers and were rewarded with goals in each half from Mario Gomez (26) and Xherdan Shaqiri (85).
Augsburg were unable to take advantage of Franck Ribery's 47th-minute red card.
Third-tier outfit Kickers Offenbach claimed a top-flight scalp as they defeated Fortuna Dusseldorf 2-0.
The game was goalless for 75 minutes before Mathias Fetsch and Stefan Vogler struck for the hosts.
Mainz edged an all-Bundesliga clash with Schalke 2-1.
Goals from Marco Caligiuri (30) and Klaas-Jan Huntelaar (75) saw the scores tied only for Nicolai Muller to win it for the visitors eight minutes from time.
Freiburg opened the scoring against Karlsruhe after just two minutes through Jonathan Schmid and that proved to be the only goal of the game.