The victory stretched their lead at the top of the Bundesliga to a staggering 16 points.
Lewandowski, who had missed Bayern’s last match with a knee injury, put Bayern 2-1 ahead with a powerful header in the 63rd minute.
He then grabbed another in the 76th with yet another header after Bremen had levelled with a Niklas Suele own goal.
In the first half, Germany international Mueller cancelled out Bremen’s lead through Jerome Gondorf and then put the final touch on Bayern’s win six minutes from time.
The forward has now netted 17 times in the Bundesliga this season.
Bayern have now collected 47 points with Bayer Leverkusen, 4-1 winners over Hoffenheim on Saturday, second on 31.
Schalke 04, on 30 points, are in action later against Hanover 96.