Robert Lewandowski scored twice to become the league’s all-time top-scoring foreign player with 197 goals. The Poland international’s former club, Dortmund, had a hard-fought 3-1 home win against Stuttgart.
Both Bayern and Dortmund have 57 points after 25 of 34 rounds with Bayern top on goal difference.
But all the momentum is with Bayern after its 12th win from 13 league games, while Dortmund — which had a nine-point lead at one stage this season — has only two wins from its last six.
Also Saturday, Leipzig was held 0-0 at home by Augsburg, and Freiburg beat Hertha Berlin 2-1.
Mainz hosted Borussia Moenchengladbach later Saturday.