It is only the second time Pep Guardiola's Bayern have lost at all this season after they went down 2-0 at Arsenal in the Champions League in October.
German Bundesliga: Buoyant Gladbach aim to dent Bayern
It was also Bayern's first Bundesliga defeat since losing 2-1 at Freiburg last May as second-half goals by Oscar Wendt, Lars Stindl and Fabian Johnson left the Bavarian giants reeling.
Franck Ribery scored Bayern's late consolation goal on his return after nearly nine months out with injury.
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