Mergim Berisha's second-half goal was the difference between the two sides and it leaves the Bundesliga champions fourth in the table after seven matches.
There were a few silver linings in defeat for Julian Nagelsmann's side - most notably the performance of Alphonso Davies - but there was an overriding sense of disappointment yet again.
It's the fourth time Bayern have dropped points in the league already this season having won just three of their opening seven games.
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Here are the winners, losers and player ratings from another poor afternoon.