The Poland international scored twice in the break-up, his second tied him with the record of 42 goals, which has stood since 1972.
The striker now has one game left, Friday at home against Wolfsburg, to break the record.
Lewandowski had a whopping eight shots on target during the match against Stuttgart as he watched Muller’s record and was rewarded twice for his effort in the second half.
The first came after a cleverly improvised first touch and then a controlled chip over the onrushing goalkeeper.
The second was a simple tap-in after some good work by Serge Gnabry on the counterattack.
Things could have gotten even better for the 33-year-old, but his 83rd-minute effort hit the post.
Despite his equal performance, Lewandowski was outmatched by his attacking partner Gnabry, who scored a hat-trick and posed a constant threat throughout the match.
Bayern are currently nine points ahead of number two Borussia Dortmund, who have played one more game.