Saarbrucken's Philipp Hoffmann tested Dortmund goalkeeper Mitchell Langerak early on, but the Bundesliga side began to take control and Julian Schieber, Kevin Grosskreutz and Jonas Hofmann all missed chances in the opening 10 minutes.
However, Schieber headed Jurgen Klopp's team ahead after Hofmann had crossed the ball into the box.
Dortmund's profligacy almost cost them when Marcel Ziemer hit the post with a powerful effort.
Ziemer then forced Langerak to save just after the break, but the away side doubled their lead through Hofmann's close-range shot.
Timo Ochs saved well from Mkhitaryan and Aubameyang as Dortmund searched for a third goal which never came.