Bayern's 2-0 loss - coupled with yet another win by Bundesliga's number one Borussia Dortmund - means the Bavarian team, which is packed with national team players, will have an even tougher time taking over the top spot.
Dortmund, the Bundesliga defending champions, beat Mainz 2-1 on Saturday, widening its distance by seven points over Bayern.
Despite the difference, Bayern Munich director of sport Christian Nerlinger is not
writing off the German league title, but admits the race is out of Bavaria's hands.
Worringly for Nerlinger, there is clear evidence of disharmony in the team as defender Jerome Boateng and midfielder Thomas Mueller -- both national team players -- engaged in a second-half shouting match.
"I'm not writing off the title, but it's not something which need concern us now. Somehow, we have to get a grip on our weakness away from home," Nerlinger said.
"We're deeply disappointed. In the first half, we made enough chances for three games. We have to take one of those chances, it would have completely changed the course of the match."
Meanwhile, Berlin's Hertha Berlin finally broke its seven-match losing streak with a 1-0 win over Werder Bremen as coach Otto Rehhagel, Bremen's former coach, enjoyed his first win in only his second game in charge.
Rehhagel's trained the Bremen team between 1981 and 1995, the Berliner Zeitung reported.
Rehhagel took over after Hertha's miseries resulted in the firing of its two previous coaches. The Berlin team was hovering at the bottom and risked being demoted to the second league, where it played for years, so Saturday's win was much needed.
The victory lifted Hertha to 15th place out of 18 teams - just one place above the danger zone where teams risk being thrown out of the first league.
In one of the biggest upsets of the weekend last placed Freiburg beat 4th placed Schalke by 2-1. The win put Freiburg in 17th place and put a dent in Schalke's ambitions of winning a first Bundesliga title.
Schalke is now 11 points behind leader Dortmund.
Dortmund coach Jurgen Klopp refused to get carried away by the seven-point lead with two months of the season still to play.
"I haven't really thought about what the seven points mean, so I could only babble some rubbish about it," he said.