Luiz Gustavo and Mario Mandzukic struck late to earn Bayern Munich a 2-0 win at Werder Bremen to maintain their side's winning start to the Bundesliga on Saturday.

Gustavo curled an effort inside the left post in the 81st minute, and Mandzukic sealed the result with his league-leading sixth goalof the season two minutes later.

"The players tested my patience a little too much, but in the end it was enough against a strong Bremen side," Bayern coach Jupp Heynckes said. "However, I had to find clear words during the break."

Artjoms Rudnevs' 20th-minute strike was enough for Hamburger SV to celebrate its 125th anniversary with a 1-0 win over Hannover.

Bayer Leverkusen enjoyed a 2-0 win at home over Greuther Fuerth, Stuttgart had a 2-0 win in Nuremberg, and Augsburg drew 0-0 at Hoffenheim, which had Sejad Salihovic sent off for a dangerous challenge late on.

Hoffenheim's players wore T-shirts in support of teammate Boris Vukcevic before their game. Vukcevic remained in a critical condition in a hospital after his car collided head on with a truck on Friday.

Defending champion Borussia Dortmund was 10 points behind Bayern before its home game against Borussia Moenchengladbach later Saturday.

"We don't need to look at Dortmund, but ourselves. If we keep playing like this, it'll be difficult to beat us," Bayern captain Philipp Lahm said.

Bayern winger Franck Ribery came closest to breaking the deadlock early in the second half, the Frenchman bamboozling Clemens Fritz before striking the post.

The irrepressible Ribery went close again in the 65th when he cut inside four Bremen defenders only to shoot narrowly wide, but it was Gustavo who finally made the breakthrough when he let fly from around 20 metres after Thomas Mueller found him in a central position outside the penalty area.

Then Xherdan Shaqiri crossed for fellow substitute Mandzukic to score and ensure Bayern continued its run of nine wins from nine competitive games this season.

"Bayern had chances beforehand, we did too. We didn't take ours, Bayern were ice cold," said former Bayern striker Nils Petersen.

Hamburg had the outstanding Rene Adler to thank for a series of crucial saves after Rafael van der Vaart set up Rudnevs to score.

"It's not possible without such a goalkeeper," van der Vaart said. "We only had a few chances, scored one. That's enough."

Didier Ya Konan almost scored a spectacular equalizer on the hour with an overhead volley, Lars Stindl had an effort cleared off the line, and Adler denied Mohammed Abdellaoue and Ya Konan late on.

"That's my job," said Adler, who could earn an international recall if he maintains his impressive early season form.

Sidney Sam opened the scoring for Leverkusen in the 50th, and Daniel Carvajal set up his second 12 minutes later.

In Nuremberg, Stuttgart striker Vedad Ibisevic capitalized on a terrible back pass from Marcos Antonio to score just seconds into the game.

Antonio almost gave away another goal in similar circumstances 10 minutes later, but Raphael Holzhauser hit the side netting. The Nuremberg defender was substituted shortly afterward.

Martin Harnik finally settled the issue in the 75th for Stuttgart's first win of the season.