The 2012 Cup winners dominated the match, as expected, but were up against a populous Wilhelmshaven defence and a superb keeper in Aaron Siegl.
Dortmund's Marco Reus as well as Robert Lewandowski, Nuri Sahin and new signing Pierre-Emerick Aubameyang all failed to beat Siegl repeatedly before Kevin Grosskreutz finally broke the deadlock in the 71st minute with a low drive.
Substitute Marvin Ducksch added another seven minutes from time to settle the visitors' nerves and Lewandowski, who vented his anger at Borussia bosses for blocking his transfer to treble winners Bayern Munich in a midweek interview, snatched his first goal of the season in the final minute.
"Obviously this was no outstanding football match," Dortmund coach Juergen Klopp told reporters. "It is clear we have to make much more out of our chances."
"But we stuck in there, scored three good goals and are through to the next round."
Bayer Leverkusen had a much easier time, crushing Lippstadt 08 6-1 with two goals apiece from Sidney Sam and Stefan Kiessling.
Hoffenheim thrashed Aumund-Vegesack 9-0 while fellow Bundesliga club Mainz 05 needed an 87th-minute goal from Eric Maxim Choupo-Moting to edge 2-1 past Fortuna Cologne.
VfL Wolfsburg eased past second division club Karlsruhe 3-1 but Freiburg needed two goals in extra time against fourth division's TSG Neustrelitz for a 2-0 win after a goalless 90 minutes.
Holders Bayern Munich are in action on Monday against fourth division club BSV Rehden.
(Reporting by Karolos Grohmann; Editing by Martyn Herman)
