Lewandowski’s 268th goal in the competition means only Gerd Muller, with 365, has scored more goals in Germany’s top flight.
Leon Goretzka and Serge Gnabry had earlier scored as Bayern extended their lead at the top of the table.
Niclas Fullkrug hit a late consolation for the hosts who remain 12th.
Second-placed RB Leipzig could cut Bayern’s lead at the top of the table to two points if they win their game in hand against Eintracht Frankfurt on Sunday (14:30 GMT).
Hansi Flick’s side were rarely troubled in Bremen, carving out a succession of good chances that ought to have produced an even more emphatic victory.
On another day Lewandowski might have scored four – hitting the post twice and the crossbar – in a typically menacing performance.
And his 32nd league goal of the season keeps former Bayern forward Muller’s single-season record of 40 goals firmly in view.
However, Muller’s overall record is still going to take some catching, with the former Bayern and Germany forward registering a goal every 105 minutes in his 427 league games.
Poland international Lewandowski, 32, is 97 goals off that landmark but has managed his 268 from 345 games at 103 minutes per goal.
Robert Lewandowski is now level with Klaus Fischer on the all-time Bundesliga top scorers list.