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 as Bayern have now collected 47 points with Bayer Leverkusen, 4-1 winners over Hoffenheim on Saturday, second on 31.
"Bremen did it really well and we were not fully there at the start," Mueller said. "But the team is always there when it has to. We are certainly not yet where we want to be."
Schalke 04 missed their chance to take over second place after Niclas Fuellkrug snatched an 86th minute equaliser for Hanover 96 for a 1-1 draw.
Schalke are third on 31, level on points with Leverkusen as well as RB Leipzig and Borussia Moenchengladbach.
(Reporting by Karolos Grohmann, editing by Pritha Sarkar)
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