The victory was never in doubt after they went ahead through Mats Hummels early on.
Elsewhere in the competition Freiburg beat Eintracht Braunschweig 2-0, Mainz beat Erzgebirge Aue by the same score and Schalke won 3-0 against Sandhausen.
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After a dreadful start to their Bundesliga campaign, Borussia Dortmund appear to have weathered the storm after going five matches without defeat.