Mario Gotze, Thomas Muller, David Alaba and Claudio Pizarro all scored for Pep Guardiola's side with summer signing Robert Lewandowski missing a late penalty, just a minute after Rogier Krohne snatched a consolation for the third-division side from the spot.
Fellow Bundesliga side Hoffenheim made even lighter work of USC Paloma with Sven Schipplock on target five times in a 9-0 win. Tarik Elyounoussi, Ermin Bicakcic, Adam Szalai and Anthony Modeste also scored for Markus Gisdol's men.
Freiburg cleared their first-round hurdle of Trier 2-0, but Werder Bremen needed extra time to get the better of Illertissen.
Under-19 European champion Davie Selke scored the decisive third goal to ensure Bremen made it through to the second round for the first time in four years.
Elsewhere, second-division 1860 Munich came from behind to beat Holstein Kiel, Aalen beat Rehden on a penalty shoot-out and Erzgebirge Aue defeated Jena 1-0. Karslruhe won at Neubrandenburg, but Fortuna Dusseldorf lost out to Wurzburg after extra-time.