Erling Haaland scored twice in the opening nine minutes but Robert Lewandowski showed he is still the finest striker in Germany with a stunning hat-trick in Der Klassiker.
Haaland gave Borussia Dortmund the lead at the Allianz Arena after just 80 seconds with a deflected strike from the edge of the area.
The Norwegian doubled the visitors' advantage seven minutes later, finishing from Thorgan Hazard's cross after a sweeping team move.
But Lewandowski was on hand to thwart his former club and pulled Bayern back on level terms by the half-time whistle. The prolific Pole poked in from Leroy Sane's cut-back in the 26th minute before slotting a penalty into the bottom corner after Kingsley Coman was felled by Mahmoud Dahoud in the area.
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