Bremen lost Milos Veljkovic to a second yellow card around the hour mark at the Allianz Arena.
Bayern leads with 70 points and has four games left. Second-place Borussia Dortmund, which plays Freiburg on Sunday, has 66 points.
Also Saturday, Augsburg thrashed relegation-threatened Stuttgart 6-0 and Bayer Leverkusen beat 17th-place Nuremberg 2-0.
Mainz beat Fortuna Duesseldorf 3-1 in a mid-table clash.
Source: FOX Sport