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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.
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."