Dortmund opened the scoring when debutant Marco Reus struck early on.
Theodor Gebre Selassie levelled with 15 minutes left for Werder, but just over five minutes later Goetze pounced to steal the points for the champions.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.