Henrikh Mkhitaryan, Marco Reus and Jonas Hofmann struck in a comprehensive win for Jürgen Klopp's side just four days after they vanquished Real Madrid 2-0.
The result will not affect the destiny of the Bundesliga title, which has already been wrapped up by Bayern, but it did show the Bavarians are fallible after a 53-game unbeaten streak was ended by Augsburg a week ago.
Klopp was delighted with his players' performance at the Allianz Arena
Bayern coach Pep Guardiola fielded his strongest team against Dortmund on Saturday, but he had rested key players in a recent 3-3 draw with Hoffenheim and 1-0 defeat to Bayern.
"I think the problem is we've already won the Bundesliga and we've just dropped off," he said. "We've got to see things the way they are."