The close-season signing from Saint-Etienne marked his first start in Germany's top flight with a hat-trick, making him only the sixth player in history to do so, while want-away striker Robert Lewandowski added a fourth with a late penalty.
Jurgen Klopp's side were not at their fluent best but Aubameyang was a magnet for the ball in goalscoring positions.
The Gabon international broke the deadlock midway through the first half with a diving header, and added two more after the break following neat link-up play with Marco Reus and Lewandowski.
Meanwhile, Hertha Berlin announced their return to the top flight in emphatic style with a 6-1 demolition of a hapless Eintracht Frankfurt.
The Bundesliga 2 champions led 2-0 with just over 30 minutes gone, and although Alexander Meier pulled a goal back before the break, four second-half strikes sealed a resounding win for the hosts.
Sami Allagui and Adrian Ramos both scored twice, with debutant defender John Anthony Brooks and substitute Ronny also finding the net.
After their third place-finish last season, Bayer Leverkusen had a comfortable start to the new campaign with a 3-1 triumph over Freiburg.
New signing Son Heung-Min impressed on his debut and got his name on the scoresheet 20 minutes, after Stefan Kiessling had opened the scoring in the first half.
Sidney Sam sealed the win for Sami Hyypia's side with a 52nd-minute strike, Leverkusen hitting their opponents on the break for a second time in five minutes.
Elsewhere, there were wins for Hannover and Werder Bremen over Wolfsburg and Eintracht Braunschweig, respectively, while Hoffenheim were held 2-2 at home by Nurnberg.