Bayern came into Tuesday's meeting at the Allianz Arena following a 4-1 thrashing by second-placed Wolfsburg last time out, and it looked as though they were facing another struggle when centre-back Jerome Boateng was sent off for a foul on Sidney Sam in the penalty box inside the first 20 minutes.
But Eric Maxim Choupo-Moting, who has scored 10 goals in all competitions this season, saw his tame spot-kick denied by Manuel Neuer diving to his left.
It seemed the visitors would be left to rue that wasted chance when forward Arjen Robben headed in Xabi Alonso's corner midway through the second period, but captain Benedikt Howedes produced a similar finish from Sam's 72nd-minute delivery to earn his team a share of the spoils.
Despite dropping points for the second time in succession, Bayern maintain their eight-point advantage at the top of the Bundesliga thanks to Wolfsburg's 1-1 draw at Eintracht Frankfurt.
Buoyed by their Bayern scalp and a run of form which included just one league defeat in 12 matches, Wolfsburg went to Frankfurt confident of beating their mid-table opposition, even with new signing Andre Schurrle absent.
But, with 58 minutes on the clock, things got uncomfortable for Dieter Hecking's men, as Stefan Aigner found the net following good work by Takashi Inui.
Frankfurt were denied a fine win two minutes from time, however, as Kevin De Bruyne turned in Marcel Schafer's cross to secure a last-gasp draw.
Third-placed Borussia Monchengladbach made the most of Wolfsburg's stalemate, though, closing to within five points of Hecking's side thanks to a 1-0 victory at home to struggling Freiburg.
And in the day's only other fixture, Mainz claimed a 1-1 draw away to Hannover.
