The Poland international's double took his tally to 94 Bundesliga goals in 114 games for the Bavarians, meaning he is now the club's all-time leading foreign-born goalscorer.
Lewandowski struck his first in the 63rd minute to put Bayern 2-1 up, an effort that drew him level with Arjen Robben on 93 league goals. The 29-year-old grabbed his second in the 76th minute to make the score 3-2 and move ahead of his Dutch team-mate.
Watch: Lewandowski gives his thoughts on returning from injury against Bremen
Earlier this season Lewandowski overtook Claudio Pizarro's haul of 87 Bundesliga goals for Bayern, although the Peruvian remains the league's all-time leading foreign goalscorer with 191. Lewandowski is currently on 168 overall, having also scored 74 times for Borussia Dortmund.
As if that were not enough, Lewandowski has now found the net in all nine of Bayern's home games in the Bundesliga this season, a feat no player in the club's history has ever previously managed.
Lewandowski was not the only one setting records at the Allianz Arena on Sunday. Fellow attacker Thomas Müller also grabbed a brace – the 20th of his league career – bringing his Bundesliga tally to 100 in his 272nd outing.
"It is nothing too special," the Germany international said afterwards. "I always hoped that I would bring as many goals as possible in my career. And come on, I'm 28, it's about time I scored my 100th."
Furthermore, midfielder Javi Martinez made his 100th Bundesliga appearance for Bayern against Bremen. Astonishingly, the Spaniard has ended up on the winning team in 85 of those matches, a success rate unrivalled by any other player to have reached that landmark in Bundesliga history.