Bundesliga matchday review

Bremen's last win over Bayern was in 2006, but the hosts held their star-studded opponents until the 72nd minute when Lewandowski first struck.

The Poland hot-shot audaciously flicked Kingsley Coman's low cross into the net with his heel before doubling the damage by firing through the legs of defender Robert Bauer and Bremen goalkeeper Jiri Pavlenka on 75 minutes.

"He is certainly the best striker in the Bundesliga and one of the best in the world," enthused Bayern director of sport Hasan Salihamidzic.

"He is simply our little firecracker."

Thomas Mueller's decoy run opened up the Bremen defence for Lewandowski, who seized the chance for a third goal in two league games.

"Werder played very defensively which didn't make things easy and there wasn't much room for us," said Lewandowski.

"We had to be patient and take our chances."

There was more good news for Bayern as Germany goalkeeper Manuel Neuer made his first appearance this season after a fractured foot.

Hamburg have also won their opening two games after a 3-1 victory at Cologne on Friday.

Elsewhere, Wolfsburg enjoyed a 1-0 victory at Eintracht Frankfurt with Daniel Didavi scoring their first-half winner.

Frankfurt's Ghana midfielder Kevin-Prince Boateng was denied a penalty after being fouled in the area, with the video assistant referee ruling he was offside.

After losing their Champions League play-off at Liverpool on Wednesday, Hoffenheim fought back twice to claim a 2-2 draw at Bayer Leverkusen.

A 4-2 defeat at Anfield means Hoffenheim will play in the Europa League group stage this season. They fell behind at Leverkusen after Brazilian left-back Wendell put the hosts ahead with a penalty on 33 minutes at the BayArena.

Hoffenheim equalised when striker Andrej Kramaric fired home just after the restart, but the scores were level for only two minutes.

Germany winger Karim Bellarabi slotted home from 12 metres to put Leverkusen 2-1 ahead before Kerem Demirbay's cross was met by Mark Uth, whose shot went in off the underside of the crossbar on 70 minutes.

Borussia Moenchengladbach conceded a goal after just 35 seconds in their 2-2 draw at Augsburg.

The game had barely kicked off when Alfred Finnbogason slotted home for Augsburg but goals by Denis Zakaria and Oscar Wendt made it 2-1 to Gladbach at the break.

However, Augsburg's new Venezuelan signing Sergio Cordova, 20, hit an 89th-minute leveller, his first goal for his new German club.

VfB Stuttgart's Germany centre-back Holger Badstuber scored his first goal in the Bundesliga since December 2009 to seal a 1-0 win at home to Mainz.

Badstuber was playing for Bayern when he last netted in Germany's top flight nearly eight years ago.

However, a horror run of injuries saw him sent on loan to Schalke last season before his contract with the Bavarians expired, leaving him to rebuild his career at Stuttgart.

Stuttgart should have finished with a 2-0 win but striker Simon Terodde slammed a penalty against the post.