With defending champions Bayern Munich, under new coach Pep Guardiola, having already enjoyed a 3-1 win at home to Borussia Moenchengladbach on Friday, 24-year-old Gabon forward Aubameyang showed why Dortmund paid French Cup winners Saint-Etienne €13m for him.
The Gabon star then converted a great pass from Robert Lewandowski on 79 minutes to wrap up his hat-trick before the Poland striker converted a penalty in the dying stages.
Korea Republic striker Heung-Min Son also scored on his first competitive appearance for UEFA Champions League side Bayer Leverkusen in their 3-1 win at home to Freiburg. Stefan Kiessling put the hosts ahead with 22 minutes gone, but Freiburg's new signing Mike Hanke levelled just before the break.
Son restored Leverkusen's lead just two minutes after the break when he fired home from close range after a final pass from Sidney Sam. Germany midfielder Sam then converted Kiessling's cross to seal the win with 52 minutes gone, while Leverkusen goalkeeper Bernd Leno protected his side's lead when he saved a 67th-minute penalty from Jonathan Schmid.
Hertha hit for six
Hertha Berlin marked their return to the top-flight after a year's absence with a 6-1 rout of Eintracht Frankfurt.
Colombia striker Adrian Ramos and Tunisia forward Sami Allagui both scored twice in the hammering at Berlin's Olympic Stadium while a first-half penalty from Eintracht Frankfurt midfielder Alex Meier was all the guests could muster.
Hanover 96 enjoyed a 2-0 win over Wolfsburg, who finished with nine men after both midfielder Maximilian Arnold and Swiss defender Timm Klose were sent off.
Arnold was shown a straight red card with just 32 minutes gone for a bad tackle on Hanover's Tunisia defender Karim Haggui, while Klose was sent off seven minutes after the break for his second yellow card.
Hoffenheim were held to a 2-2 draw at home to Nuremberg while Werder Bremen enjoyed a 1-0 win at newly-promoted Eintracht Braunschweig with Austria midfielder Zlatko Junuzovic hitting the 82-minute winner.
On Sunday, Mainz host Stuttgart while Hamburg visit Schalke.