The visitors had a bright start on the road and they should have grabbed the lead but Thorgan Hazard was unable to overcome Dortmund goalkeeper Roman Buerki following a one-on-one with 10 minutes into the game.
Dortmund responded in style and broke the deadlock through Maximilian Philipp, who volleyed home Aubameyang's cross at the near post with 28 minutes played.
Maximilian Philipp remained in the thick of things as he doubled the lead for the "BVB" only 10 minutes later.
Things went from bad to worse for the visitors before the break as Dortmund tripled their advantage when Aubameyang capitalized on an assist from Philipp in the 45th minute.
Peter Bosz' men remained in control of the proceedings and extended their lead four minutes into the second half as Aubameyang tapped home a rebound to make it 3-0 on the scoreboards.
The Gabon international wasn't done with the scoring and added another goal as Mahmoud Dahoud's pass into path allowed Aubameyang to sew up his hat-trick in the 62nd minute.
With the win, Dortmund remain atop the standings meanwhile Monchengladbach slumped to ninth place.
The "Bulls" secured all three points on home soil as goals from Jean-Kevin Augustin and Timo Werner smoothed the way for the 2-1 victory over Eintracht Frankfurt.
Hence, the hosts would not have to wait for long to open the scoring as Timo Werner's shot on target was parried allowing Jean-Kevin Augustin to slot home the opener at the far post with 28 minutes into the game.
Timo Werner cut a better figure in front of Frankfurt's goal in the 68th minute as the German international benefited on a assist from Augustin to slot home into the far post corner from the edge of the box.
In the dying minutes of the clash, Frankfurt were able to reduce the arrears as Ante Rebic slotted home his first goal of the season. However http://www.redskinsfansstore.com/Redskins-Mason-Foster-Draft-Jersey/ , the hosts were able to protect their lead to the end to secure the third win of the season.
With the result, Leipzig climb on sixth place while Frankfurt stay on 10th.