Bayern, the 2013 and 2014 cup winner, was made to work hard for a 3-1 win over fifth-tier Noettingen in Karlsruhe.
New signing Arturo Vidal scored from the penalty spot in the fifth minute, one minute before the Chile star was booked for a crunching tackle.
Niklas Hecht-Zirpel claimed a personal highlight in the 16th by equalizing on the rebound after Bayern ‘keeper Sven Ulreich parried his first effort.
Noettingen regrouped and did well to frustrate Bayern in the second half.
Henrikh Mkhitaryan scored one and set up another as Dortmund beat third-division side Chemnitzer FC 2-0.
The Armenia midfielder crossed for Pierre-Emerick Aubameyang to score with a fine header in the 25th, and Aubameyang returned the favor for Mkhitaryan to seal the win with a curling shot inside the far post in the 83rd.
Jena upset Hamburg 3-2 thanks to Johannes Pieles’ extra time-winner.
Justin Gerlach put the fourth-tier side ahead with a poorly defended free kick in the 15th before Albin Ekdal equalized in the 48th, though TV replays showed the ball was out of play before Ivo Ilicevic crossed.
Velimir Jovanovic restored Jena’s lead in the 58th, but Michael Gregoritsch scored in the fourth minute of injury time to take the game to extra time.
Mainz beat third-division Energie Cottbus 3-0, and Hannover defeated fourth-tier Hessen Kassel 2-0 thanks to goals from Salif Sane and Kenan Karaman.
Nils Petersen scored four goals as Freiburg routed fifth-tier Barmbek-Uhlenhorst 5-0, while another second-division team, Bochum, thrashed fifth-tier Salmrohr by the same score.
Fourth-tier Unterhaching upset promoted Bundesliga side Ingolstadt 2-1, second-division Paderborn won 2-1 at fourth-tier Luebeck, and second-division Heidenheim routed fourth-tier FK Pirmasens 4-1.
Second-division sides Sandhausen and Fortuna Duesseldorf needed penalties to advance after being held scoreless by fourth-tier opposition. Sandhausen defeated Bahlinger SC 5-3 and Duesseldorf beat local rival Rot-Weiss Essen 3-1. Both Sandhausen and Duesseldorf finished with 10 men.
Second-division Kaiserslautern defeated third-division rival Hansa Rostock 5-4 on penalties. Former Kaiserslautern striker Marcel Ziemer’s penalty miss proved the decisive one.