First half goals from Donyell Malen (23), who fired a low shot in off the posts, Jude Bellingham (19) and Karim Adeyemi (20) quickly put the visitors in the driving seat against the third division club.
See the statistics and information from the game on Flashscore
The Ruhr valley club, desperate to break Bayern Munich's decade-long stranglehold on the league title, were without new striker Sebastien Haller (28), who has undergone surgery for a tumour in his testicle and will be sidelined for several months.
Haller was brought in to fill the gap left by forward Erling Haaland, who joined Manchester City.
Still it was one-way traffic towards the Munich goal in front of 12,000 fans at the Gruenwalder stadium in the first half, with Dutchman Malen wreaking havoc down the left and forcing an early substitution by the hosts.
Dortmund, who face fellow Champions League club Bayer Leverkusen in their Bundesliga opener on Aug. 6, took their foot off the gas after the break but forced Munich keeper Marco Hiller to make a string of superb saves to stop shots from Mo Dahoud, Marco Reus and Thomas Meunier.
Fellow Bundesliga club VfB Stuttgart also booked their spot in the second round following a 1-0 at Dynamo Dresden, while Nuremberg and Karlsruhe joined them after their victories over fourth and fifth division opponents respectively.
Champions Bayern Munich meet Cup winners RB Leipzig in the German Super Cup on Saturday before the Bundesliga season starts next week.
