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It took Dortmund just nine minutes to take the lead as their clinical attack broke at pace with Mkhitaryan, whose low cross could only be parried by Felix Wiedwald, which allowed Marco Reus to fire home from close range.
Thomas Tuchel's side dominated for long spells after breaking the deadlock, and they threatened to double their advantage when Mkhitaryan's powerful strike was beaten away by Wiedwald.
Werder came back into the game impressively to equalise with a patient passing move as the hosts worked the ball into the box, before Anthony Ujah slotted in after Florian Grillitsch's effort had been charged down.
However, the lead belonged to Dortmund once again as Mats Hummels produced an inch-perfect cross to give Mkhitaryan the easy task of heading home.