The German giants were bested at home after Bayern claimed a 1-0 win thanks to an impressive 20-yard chip shot from Joshua Kimmich in the first half.
Dortmund are reeling after news that striker Erling Haaland suffered an injury in the game.
He came off with 20 minutes remaining in the match. Haaland limped away and has suffered a knee injury.
Manager Lucien Favre told a post-match news conference: "I don't think he'll be out for long.
"He's got a knee injury. We don't know at the moment exactly what it is."