Jurgen Klopp's men produced a trademark display of powerful counter-attacking football and the game was essentially out of sight by half-time as Dortmund raced into a 3-0 lead at the Turk Telekom Arena.
Pierre-Emerick Aubameyang opened the scoring when he applied the finishing touch to Marco Reus' excellent low delivery and the Gabon international doubled his tally shortly before the 20-minute mark.
There was a sour note for Dortmund when Sven Bender was forced off with an apparent elbow injury in the second half, but Adrian Ramos' goal a minute after coming as a substitute completed the rout.
Dortmund were finding gaps in the home defence with ease and Shinji Kagawa should have done better when he shot tamely at Muslera when one-on-one, while Aubameyang wasted a chance for his hat-trick when he inexplicably hit the post with the goal gaping from Mkhitaryan's delivery.
However, the third arrived four minutes before half-time when Reus let fly with an unstoppable 25-yard shot that crashed over Muslera's despairing dive and in.
Dortmund had to replace Bender with Matthias Ginter in the 55th minute, but it failed to disrupt the away side's flow and Reus should have hit the target when his half-volley deep inside the penalty area flew high into the stands.
But Ramos capped the result in the 83rd minute as he collected fellow substitute Ilkay Gundogan's throughball and kept his cool to give Dortmund a huge shot in the arm ahead of a home game against Hannover when they return to domestic action this weekend.
