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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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.