After an encouraging start from the hard-tackling home side, Lewandowski opened the scoring with a penalty in the 37th minute after goalkeeper Rene Adler brought down Thomas Mueller just inside the area. Adler picked up Hamburg's third yellow card and Lewandowski's score was Bayern's only shot on goal in the first half.
The Poland striker claimed his second - his 17th of the season - in the 61st, when he deflected Mueller's volley past the helpless Adler, eight minutes after Aaron Hunt's free kick somehow found its way in for Hamburg.
Bayern defender David Alaba struck the post with a free kick minutes after what proved Lewandowski's winner. Bayern moved 11 points clear of Borussia Dortmund ahead of the rest of the 18th round. Dortmund visits Borussia Moenchengladbach on Saturday.
Hamburg coach Bruno Labbadia, who was in his first stint in charge when the side last defeated Bayern on Sept. 26, 2009, was furious that his team was left empty-handed despite limiting the visitors' chances.
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Bayern looked rusty after the 33-day break yesterday. The visitors had to cope without the injured Mario Goetze, Franck Ribery, Medhi Benatia, Rafinha and Juan Bernat. Arjen Robben made a late substitute appearance, while defender Jerome Boateng went off with a groin injury in the 56th. Bayern said Boateng would undergo an examination back in Munich to determine the severity of the injury.
"We could have played a little better but I'm satisfied," Mueller said. "We knew we weren't at our best level but we knew we were at a level where we could compete and win the game. We'll improve from game to game."
The Spanish coach has announced his intention to leave for the Premier League after completing his three-year deal.