Bayern, who had won their last 14 Bundesliga matches, had five players booked and full-back Rafinha sent off in a surprisingly feisty encounter which saw their goalkeeper Manuel Neuer save a Robert Lewandowski penalty.
With Bayern already having won the title and Dortmund guaranteed a Champions League place next season, there had been fears that the match would be a damp squib as the teams spared themselves for Wembley.
Lewandowski's shot was saved by Neuer, but the match boiled over again a few minutes later when Rafinha, who had just been booked, elbowed Jakub Blaszczykowski as they tussled for the ball.
The Brazilian was sent off for a second bookable offence, causing more Bayern protests as the players angrily surrounded the referee, and Rafinha poked his finger in Blaszczykowski's face before leaving the pitch.
Dortmund coach Jurgen Klopp remonstrated with Rafinha, which in turn caused an angry reaction from Bayern's sporting director Matthias Sammer.
"It's normal for these things to happen," Klopp told Sky on the touchline. "People were talking about a friendly but once the game gets underway, it's different. It was a tough battle, situations arise, these things happen."
"I told Rafinha that he should stay away from Jakub, Sammer then told me that I should not talk to the players. Then I said that Rafinha poked him in the face."
Dortmund went ahead in the eleventh minute when Kevin Grosskreutz volleyed in Blaszczykowski's cross at the far post.
Mario Gomez headed Bayern level on 23 minutes when he headed in unmarked at the far post from Rafinha's cross.
"After last week's result it wasn't easy to get back into the swing of things," said Bayern coach Jupp Heynckes.
"It was a very intensive game where neither side gave anything away. Beforehand, people said that it would be a boring match with so many Bayern players missing, but that clearly wasn't the case."
