The match brought together the reigning league champions of England and Germany, with Bayern controlling the opening stages and putting City under sustained pressure.
The hosts took the lead in the 11th minute when Linda Dallmann played a through ball to an unmarked Giulia Gwinn, who calmly finished past City goalkeeper Ayaka Yamashita.
Bayern doubled their advantage 16 minutes later after City defender Kerstin Casparij made an error while attempting to clear the ball. With no opponent immediately around her, Casparij sliced her clearance into her own goal.
City responded shortly before half-time when Beth Mead pulled one back from close range. Khadija Shaw's shot deflected into the England international's path, allowing Mead to prod the ball into the net.
The goal sparked controversy after a blue smoke bomb had been thrown onto the pitch. Bayern players argued that play should have been stopped before City's attack resulted in the goal.
Manchester City were then handed a chance to level the match after Bayern goalkeeper Ena Mahmutovic brought down Aoba Fujino inside the penalty area. Shaw stepped up to take the resulting spot-kick, but Mahmutovic recovered from her mistake with an excellent save to deny the powerful effort.
City continued to push for an equaliser and were eventually rewarded late in the match. Germany international Carlotta Wamser scored her first goal for the club, sending a low shot beyond Mahmutovic to make it 2-2.
Bayern had opportunities to reclaim the lead in the closing stages, but substitute Edna Imade failed to find the target with two good chances.
The German champions had appeared firmly in control during the opening 40 minutes and could have built an even bigger advantage. Klara Buhl and Pernille Harder both missed opportunities, while Yamashita also made an important save from Buhl.
Jovana Damnjanovic fired over from a promising position, while Momoko Tanikawa missed two chances to extend Bayern's lead. City also threatened when a deflected Lauren Hemp cross struck the top of the crossbar.
After Mead's goal, City grew in confidence and became the stronger side. Despite Shaw's missed penalty, Wamser's late equaliser secured a valuable point.
Bayern will travel to Portugal to face Benfica on Sept. 30, while Manchester City will host Real Madrid on Oct. 1.
