The forward doubled his tally to put the match beyond doubt midway through the second half, guiding home a cool finish after collecting a precise through-ball from Marco Reus.
Augsburg were unable to find a way back into the match despite the best efforts of Sascha Molders, who worked tirelessly in attack without managing to take any of the half-chances created by Halil Altintop.
Reus continued to push for a third in the closing stages alongside substitute Jakub Blaszczykowski, with the visitors soon able adding shine to an opening-day win through Aubameyang.
The summer signing made no mistake to complete his hat-trick from close range, rounding the goalkeeper after collecting a flick from Robert Lewandowski.
Lewandowski then opened his account four minutes from time, guiding a penalty kick into the corner to get Dortmund's fourth goal of the day.