BERLIN: A first-half strike from Douglas Costa was enough for defending champion Bayern Munich to edge Wolfsburg 1-0 at home and scrape into the German Cup quarter-finals on Tuesday.

Costa scored with a deflected shot in the 18th minute but Bayern failed to build on its greater possession and was made to suffer late on as Wolfsburg grew in confidence.

Yunus Malli should have equalised with less than 10 minutes remaining when Manuel Neuer saved in a one-on-one and the Bayern 'keeper was called into action again to deny Daniel Didavi.

Late substitutions helped Bayern hang on and take the momentum from Wolfsburg, but there were whistles from home supporters unhappy with the display.

"For 80 minutes we did well," Bayern coach Carlo Ancelotti said.

Ancelotti has come in for some criticism following a dip in performance lately and the first dropped points in the Bundesliga after seven games at the weekend.

The Italian gave an indication of his likely lineup for Arsenal's visit in the Champions League next week - with no room for misfiring Thomas Mueller, while Thiago Alcantara returned from injury and Philipp Lahm and David Alaba also started.

Lahm, the Bayern captain, announced after the game that he is retiring at the end of the season, one year before his contract with the club ends in 2018.

"It's just a few more months, but no more," said the 33-year-old Lahm, who was honored before the game for making his 500th appearance in a competitive match for Bayern at the weekend.

The former Germany captain, who retired from international football after winning the World Cup in 2014, said he had been considering the decision for more than a year.

Hamburger SV 2, Cologne 0

American forward Bobby Wood sealed Hamburger SV's progress to the quarter-finals with the winning goal.

Wood intercepted a wayward pass from Pawel Olkowski in midfield, sprinted forward and played a one-two with Gideon Jung before staying cool in front of Cologne 'keeper Thomas Kessler to score with 15 minutes remaining.

Hamburg's Luca Waldschmidt had hit the post a minute before.

Jung got the home side off to a flying start in the fifth minute but Cologne came close to equalizing through Anthony Modeste.

Greuther Fuerth 0, Borussia Moenchengladbach 2

An early goal from Oscar Wendt set 'Gladbach on its way and the visiting side's task was made easier when Hungary midfielder Adam Pinter was sent off with a straight red card for a bad challenge on Christoph Kramer in the 18th.

Thorgan Hazard completed the scoring against the second-division side with a penalty before the break.

Astoria Walldorf 1, Arminia Bielefeld 1

Second-division Bielefeld won 5-4 on penalties after fourth-tier Walldorf equalised late through Marcel Carl to take the match into extra time.

Bielefeld's Keanu Staude was sent off with his second yellow card 20 minutes after coming on in extra time but Walldorf, which had upset Darmstadt and Bochum in the previous rounds, went out when Stephan Salger converted the decisive penalty in the shootout.