Gladbach had no answer to Peter Bosz's fleet-footed Dortmund, who opened a two-point lead over Hoffenheim at the top in a perfect confidence boost before Tuesday's Champions League clash with holders Real Madrid.
Aubameyang, last season's top scorer in Germany's top flight, has now netted eight goals in six league games — one ahead of main rival Robert Lewandowski of Bayern Munich.
Dortmund thrash Hamburg to claim top spot
Left winger Maximilian Philipp scored Dortmund's first two goals before Aubameyang's hat-trick, with defensive midfielder Julian Weigl scoring a superb sixth.
"We were very dominant. It was an intense game and we can be very satisfied," said Philipp, who also scored two goals against Cologne last weekend.
Weigl was delighted to score on only his second game back from injury.
Beating Dortmund ‘massive’ for confidence: Pochettino
"It feels great, the goal was the icing on the cake," said the Germany midfielder. "We were lucky that Gladbach did not use their chances and usually they have the quality to fix problems."
After third-placed Bayern threw away a two-goal lead on Friday in a 2-2 draw at home to Wolfsburg, Dortmund are now three points ahead of the defending champions.
Bayern could finish the weekend in fourth if Hanover 96 beat bottom side Cologne on Sunday.
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