The weekend was also marked by controversy as Hoffenheim were denied a Kevin Volland goal in their 2-2 draw against Nuremberg despite replays showing that the ball crossed the line before bouncing out.
The incident is bound to raise the issue of goal-line technology in Germany, which the country's football federation has said it will not use until at least 2015.
Gabon international Aubameyang, who joined from France's St Etienne for a reported 13 million euros in July, put the visitors ahead with a diving header in the 24th minute and slotted home from the left midway through the second half.
The 24-year-old completed his remarkable debut by picking up a superb Robert Lewandowski pass to round Augsburg goalkeeper Mohamed Amsif 11 minutes from time.
"That was a super start for me," a beaming Aubameyang told reporters. "The intensity in the league here is much higher than in France. Our aim is to work hard and see what is possible in this season."
Poland international Lewandowski, who had wanted to move to Bayern Munich but saw the transfer blocked by his club, got onto the scoresheet himself with an 86th minute penalty.
"I told my players it would be tough and there are not many teams who will win 4-0 here," Dortmund coach Juergen Klopp told reporters. "We scored some great goals and finished off the game."
SIX-GOAL HERTHA
Hertha Berlin made a sensational return to top flight in front of a 55,000 home crowd in the Olympic stadium, crushing Eintracht Frankfurt 6-1 with Sami Allagui scoring two goals in two minutes and Adrian Ramos adding two more.
Hertha also hit the woodwork three times in the first half.
Champions League participants Bayer Leverkusen, third last season, struck twice early in the second half in a 3-1 win over Freiburg, who had cancelled out Stefan Kiessling's opener with a Mike Hanke goal just before the break.
Two goals from South Korea's Heung Min-son and Sidney Sam in the 46th and 52nd minute killed off Freiburg's hopes of a point.
Hanover 96 beat nine-man VfL Wolfsburg 2-0 after the visitors had Maximilian Arnold and Timm Klose sent off.
Promoted Eintracht Braunschweig's return to the Bundesliga after 28 years was spoiled by a 1-0 Werder Bremen win with Zlatko Junuzovic snatching the goal eight minutes from time.
Defending champions Bayern Munich launched their season with a 3-1 win over Borussia Moenchengladbach on Friday. ($1 = 0.7490 euros)
(Reporting by Karolos Grohmann; Editing by Brian Homewood)
