The Gabon international took his league tally to eight goals from six matches as Dortmund enjoyed a flawless dress rehearsal for next week's Champions League group match against Real Madrid.
The Ruhr valley club now have the best goal difference after six matches in Bundesliga history with 19 goals scored and one conceded and have quickly established themselves as credible title contenders.
"We played really well with the ball and off the ball," Dortmund coach Peter Bosz told reporters.
"It was a team effort above all. I can only pay a compliment to my team with this performance coming only three days after Hamburg (Dortmund's midweek Bundesliga win)."
They gave Gladbach no chance with their high-tempo game and hit the woodwork twice before the talented Philipp grabbed two goals in 10 minutes.
Last season's Bundesliga top scorer Aubameyang then struck either side of the break for his own double and made it three goals with a superb solo run in the 62nd minute.
The hosts conceded their first goal of the season four minutes later but Dortmund's Julian Weigl capped his first start since a four-month injury break with his first ever Bundesliga goal, a sensational 20-metre strike in the 79th.
Dortmund have 16 points, three more than third-placed Bayern Munich, who wasted a two-goal lead on Friday to draw 2-2 against VfL Wolfsburg.
Hoffenheim beat Schalke 04 2-0 with a goal in each half on Saturday to move into second place on 14 with their fourth win in six matches.
RB Leipzig, last season's runners-up, beat Eintracht Frankfurt 2-1 for their first win in three matches and climbed to sixth on 10 points.
(Reporting by Karolos Grohmann; Editing by Toby Davis and Clare Fallon)
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