Forward Adrian Ramos also scored his first competitive goal since joining from Hertha Berlin this season and Henrikh Mkhitaryan added another with Dortmund in full control for the entire game.
Fellow Bundesliga club VfB Stuttgart crashed out, slumping to a 2-0 defeat to second division club VfL Bochum.
New signing Simon Terodde, who joined from Union Berlin, scored both goals for Bochum as Stuttgart coach Armin Veh suffered a disappointing return to the Stuttgart bench.
His team became the second top tier club to exit the competition at the first hurdle after Mainz 05 were eliminated on penalties against Chemnitz on Friday.
Swedish forward Branimir Hrgota scored twice and newly-signed striker Andre Hahn added another as Borussia Moenchengladbach eased past regional club Homburg 3-1 to book their spot in round two.
They were joined by Hertha Berlin who beat Viktoria Cologne 4-2 and Hanover 96 who had little trouble disposing of Astoria Walldorf 3-1.
Holders Bayern Munich are in action against third tier Preussen Muenster on Sunday.
(Reporting by Karolos Grohmann; editing by Josh Reich)
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