BERLIN - Robert Lewandowski's clinical finishing steered Bayern Munich to a 3-1 win at Bavarian rival Augsburg that restored the side's eight-point lead in the Bundesliga on Sunday.

Lewandowski scored two goals, starting with the visitors' first real chance in the 15th minute when he took Thomas Mueller's cross with his right foot, turned with a left-foot touch and fired the ball inside the far post with his right.

Douglas Costa tested Augsburg 'keeper Marwin Hitz with a free kick before the break, while Bayern goalkeeper Manuel Neuer had little to do at the other end.

Lewandowski settled the match with his second goal in the 62nd, picking his spot in the far corner after Thiago Alcantara played a perfect 30-meter (yard) pass into his path. It was the Poland striker's league-leading 21st goal of the season.

Hitz pulled off a good save to deny Arjen Robben, but he was powerless to prevent Mueller from claiming his 86th goal for Bayern in the 78th.

Raul Bobadilla eluded three defenders to score Augsburg's consolation in the 86th.

"Of course it's incredibly difficult to stand up to such a strong team. It's a shame, but you can say they're not the games in which we absolutely have to get the points," Augsburg captain Paul Verhaegh said.

Bayern players took to the pitch wearing T-shirts with Holger Badstuber's name and number on their backs and "We're with you. You'll manage it again" written on their fronts, following the defender's latest serious injury. Badstuber was ruled out for three months after fracturing his ankle in training on Saturday.

"We love Holger. He's a super guy, a great player. It's not normal, the bad luck he's had. And what happened yesterday, when he was alone, incredible. He knows we're always there for him," Bayern coach Pep Guardiola said.

Franck Ribery was back in the squad for the first time since playing Dinamo Zagreb on Dec. 9 but the French winger stayed on the bench.

Earlier, Ivo Ilicevic came off the bench to secure a 3-2 victory for Hamburger SV over Borussia Moenchengladbach that ended his side's run of six league games without a win.

"We got three points, no more and no less, but it was a very, very important win," said Hamburg coach Bruno Labbadia, whose side moved six points clear of the relegation zone.

United States international Fabian Johnson put visiting Moenchengladbach ahead in the 14th minute with his fifth goal of the season.

'Gladbach was in control but an own goal from Martin Hinteregger drew the home side level in the 38th and Hamburg striker Artjoms Rudnevs made it 2-1 three minutes later off a long kick from goalkeeper Rene Adler.

"We gave the game away," 'Gladbach sporting director Max Eberl said.

Ilicevic sealed the win in the 80th, heading home from close range after Spahic headed on a corner.

There was still time for Raffael to score 'Gladbach's consolation in the 88th.