Ramy Bensebaini scored twice for the hosts who are top of the Bundesliga, seven points ahead the Bavarians.
It is Bayern’s second consecutive defeat under interim coach Hansi Flick, and even though they boast the league’s top scorer in Robert Lewandowski, with 16 goals, Joshua Kimmich blamed the team’s finishing.
“It’s bothering me so much, I could go crazy,” said Kimmich. “When you miss so many good chances, it’s not just always bad luck.
“I don’t know what’s lacking. We have the quality to get the most out of our chances.”
Borussia Dortmund’s English winger Jadon Sancho’s name keeps being linked with top Premier League sides like Chelsea and Manchester United, but the speculation is not affecting his performance.
After Sancho had been dropped for the Champions League game against Barcelona in November for “lacking focus” he has maintained his sparkling form when given the opportunity.
Sancho scored twice as Dortmund thrashed Fortuna Dusseldorf 5-0 on Saturday.
“We’re continuing to plan with him,” said Borussia Dortmund sporting director Michael Zorc before the game. “He’s a fundamental player for us and I do not see any scenario where he leaves us.”
Florian Kohfeldt hoped Werder Bremen turned a corner with a win at VfL Wolfsburg last weekend after a difficult start to the season.
Kohfeldt described the game as “brutally important” but his team did not respond and conceded a stoppage time goal to Sven Michel, which VAR ratified after a four minute wait.
Werder have vital clashes coming up against FC Koln and Mainz 05 which will confirm if the young coach, 37, is about to hit his first crisis or their struggles are just a blip.
Reporting by Rik Sharma; Editing by Christian Radnedge