The Poland international, who narrowly missed out on being top scorer last season, snatched his first goal in the 72nd minute with an audacious backheel and added another with a fine solo effort before Werder had time to recover.
The hosts had managed to keep Bayern at bay for much of the game but gradually, as expected, ran out of steam as the reigning champions launched a relentless assault on their defence. The Bavarians, who have now won their last 16 games against Werder in all competitions, are on six points, the same as Hamburg SV, who won 3-1 at Cologne on Friday.
La talonnade géniale de Robert Lewandowski (Bayern Munich) au Werder de Brême
Image credit: Getty Images
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Former Bayern defender Holger Badstuber scored the winner for his new club VfB Stuttgart as the promoted team got their first three points of the season with a 1-0 win over Mainz 05.
It was Badstuber's first goal since 2009 with the former Germany international having been plagued by injuries.
Eintracht Frankfurt will be asking themselves how they lost to VfL Wolfsburg 1-0 after rattling the woodwork repeatedly, wasting a hatful of chances and having more shots on goal in the first half than in any game of the last three seasons.
Venezuelan Sergio Cordova's 89th-minute goal rescued a point for Augsburg with a 2-2 draw against Borussia Moenchengladbach while Bayer Leverkusen and Hoffenheim also shared a draw by the same score.
Borussia Dortmund are in action later against Hertha Berlin.
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