Augsburg needed extra-time to see off minnows Elversberg 3-1 and avoid an embarrassing first-round DFB-Pokal exit on Friday.
The Bundesliga side were overwhelming favourites to defeat the fourth-tier side, but fell behind to Kevin Maek's 52nd-minute strike.
With the clock winding down, Raul Bobadilla levelled with seven minutes remaining and Elversberg's challenge was made more difficult by a red card in injury time for Markus Obernosterer.
The numerical advantage soon told in the additional 30 minutes as Sascha Molders put Augsburg ahead, and Tobias Werner added gloss to the scoreline in the second half of extra-time.
Bundesliga new boys Darmstadt had no such problems as they battered Erndtebruck 5-0, Dominik Stroh-Engel scoring twice for the visitors at the Leimbachstadion.
Second-tier side FSV Frankfurt were 2-0 victors at BFC Dynamo.
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