The new signing from St Etienne scored three as Jurgen Klopp's men responded in style to Bayern Munich's 3-1 win over Borussia Monchengladbach last night to keep pace with the Bavarians at the top of the table.
Augsburg gave last season's runners-up a stern test but ultimately the difference in quality between the two sides shone through, thanks to the Gabon international and a late Robert Lewandowski penalty.
Aubameyang gave the first glimpse of why Dortmund had chosen him to replace Mario Gotze when he burst through after just 30 seconds, but he chose to pull the ball back to Lewandowski and his pass was intercepted.
There was only one thing on his mind in the 26th minute, though, when he headed Dortmund in front from Marcel Schmelzer's cross.
Augsburg reacted well and searched for a route back into the game, although Dortmund goalkeeper Mitchell Langerak, in for the suspended Roman Weidenfeller, was rarely tested.
The Australian goalkeeper has a remarkable record of having been on the winning side in each of his 10 previous Dortmund appearances, and that was a statistic which would be extended thanks to Aubameyang.
He added a second midway through the second half, picking up Marco Reus' pass to fire into the far corner, before completing his hat-trick with a fine individual effort, taking the ball round Mohamed Amsif before stroking it into the unguarded goal.
He was then given a standing ovation as he was replaced by Jonas Hofmann, who almost immediately earned a penalty.
Lewandowski, who had been shifted into the shadows by Aubameyang, stepped up to the spot to open his account for the season and complete the rout.