Jurgen Klopp's men earned all three points despite playing with a numerical disadvantage after goalscorer Ivan Perisic was sent off early in the second half
A first-half strike by Ivan Perisic, who was sent off in the early minutes of the second period, and a goal by Patrick Owomoyela after the break was enough to lift BVB over the Green-Whites.
Chances were few and far between for both teams before the 20-minute mark, when a blast from distance by Claudio Pizarro sparked the match into life. Thomas Schaaf's men began to play more aggressively once BVB opened up, and went close to scoring on a couple of occasions.
Out of nowhere, Dortmund took the lead. A quick break saw Gotze and Robert Lewandowski charge forward with the Polish striker picking out Sven Bender. He then found Perisic, who powered a superb shot from the left side of the box past Sebastian Mielitz.
The second half could not have started worse for BVB as Perisic was sent off moments after the restart as he committed a needles foul on Sokratis Papastathopoulos and received his second yellow card.
Later in the second half, Dortmund delivered the final blow as some poor defending by the home side allowed Hummels to find Owomoyela near the right post, and the full-back stabbed a finish in the upper corner to double BVB's lead.
The Green-Whites threw everything forward in the remaining minutes, but were ultimately denied even a consolation goal by Borussia Dortmund's water-tight defense.