The Pole matched Klaus Fischer's tally of 268 goals as he joined Leon Goretzka and Serge Gnabry on the scoresheet in a comfortable win that extended the champion's lead at the summit to five points.
Lewandowski now needs another 97 goals to match Bayern legend Gerd Muller's incredible tally of 365.
Werder was given hope that it might put Bayern under pressure when Ludwig Augustinsson produced the first shot on target of the match, cutting in before releasing a weak right-footed effort.
But it was all Bayern from there, with Gnabry and Joshua Kimmich signalling the visitors' intent as they each fired just over the bar in quick succession.
Despite repeatedly hitting the post and crossbar, Lewandowski finally scored with an hour gone.
Only a superb save from Bremen goalkeeper Jiri Pavlenka also prevented Lewandowski scoring with a powerful header late on.
The victory extends Bayern's lead at the top of the table to five points.
Second-placed RB Leipzig is now under pressure to beat Eintracht Frankfurt at home on Monday (AEDT) to keep pace with the Bavarian side.