Bayern coach Ottmar Hitzfeld said he was disappointed with his team's performance in front of a derby crowd of 69,000 but said they were already thinking about the match in Glasgow they need to win to avoid risking an early exit.
Despite the seventh consecutive derby win, Bayern remained in fourth place, six points behind first place VfB Stuttgart.
Stuttgart extended their unbeaten tally to 13 matches with their 10th triumph, a 3-1 victory over Hanover 96. Werder Bremen rose to second ahead of Bayer Leverkusen with a 3-1 win over VfL Bochum. Leverkusen and fifth-placed Borussia Dortmund drew 2-2.
"We've got the Champions League match in Glasgow on Tuesday and that's the top priority," Hitzfeld said. "I'm satisfied with today's result but not the performance. We weren't concentrated, we weren't fired up enough and we lost the ball far too much.
Bayern lie third in Champions League Group A with two group games left and need points to avoid making an early exit from the competition for the second year in a row. Celtic thrashed Dundee United 5-1 in the Scottish premier league.
In Saturday's derby against eighth-placed 1860, Netherlands striker Roy Makaay scored his seventh goal of the season for Bayern from their only first-half shot on target.
It took an impressive save by goalkeeper Oliver Kahn late in the match from a Benjamin Lauth shot to prevent 1860 from earning the draw.
"If we want to survive (in the Champions League) we're going to have to play a lot better than we did today," Kahn said.
Bayern were missing the creative midfield talents of Sebastian Deisler and Mehmet Scholl. Deisler is being treated for depression while Scholl has a back injury.
They also had to play the final 30 minutes without Bosnia midfielder Hasan Salihamidzic, who was controversially sent off for a foul along with 1860's Andreas Goerlitz after the pair were involved in some theatrical diving.
"I think we won a moral victory today," said 1860 trainer Falko Goetz. "We didn't want to just sit back and play for a draw but went after them and tried to win the derby."
Stuttgart tuned up for their Champions League game against Rangers with an easy 3-1 win against Hanover. Silvio Meissner scored twice after Imre Szabics put the team in front for their eighth consecutive win at home.
The biggest cheers of the day came before the match began when Stuttgart announced that Germany international Andreas Hinkel, one of the keys to Stuttgart's surprising run, had signed a contract extension.
"We're having a great run," said Stuttgart coach Felix Magath. "Even with players sidelined with injuries we're able to keep up the level of performance."
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