Die Borussien, who were beaten by Hamburg last week and lost to Krasnodar in the Europa League on Thursday, looked in no mood to endure another defeat as they dominated possession from the start at Signal Iduna Park.
The Polish keeper was beaten moments later though as Gonzalo Castro nodded the ball into the net.
Castro then turned provider on 19 minutes when he teed up Aubameyang and rifled the ball high into the roof of Tyton's goal.
Didavi cropped up with five minutes of the half left to score for Jurgen Kramny's men and give VFB hope of a comeback.
Aubameyang nearly scored his second in the 50th minute, but could only direct the ball past the left post after Mkhitaryan's through-ball.
Dortmund's third eventually came after 65 minutes, when Niedermeier diverted a pass into the area into his own net.
They continued to dominate into the closing stages, with Aubameyang seeing his shot saved just minutes before Marco Reus missed the target from close range.
With seven minutes remaining, a cross fell to Mkhitaryan but the Armenian international missed the target.
Aubameyang completed the scoring in stoppage when his shot nestled into the bottom-right corner.