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The relegation strugglers came close again minutes later when midfielder Hakan Calhanoglu smashed a shot towards goal with Manuel Neuer looking beaten, only for the player to see the ball scrape wide of the post.
Bayern took the lead with their first meaningful chance after 32 minutes, when Mario Gotze latched on to Arjen Robben's cross to tap into the net and leave Munich to surpass Werder Bremen's previous record of 43 away goals in one season.
Hamburger could have pulled level just before half time, but Neuer pulled off a world-class save to tip over Rafael van der Vaart's dipping volley from distance.
SV's hopes of clinching an important victory were dealt a major blow after half time, when Gotze rifled in a half-volley which brushed Thomas Muller on its way into the net.
Gotze grabbed his second of the afternoon to make it 3-0 after 69 minutes, before Hamburger pulled a goal back through Calhanoglu's fine strike.
Bayern compounded the hosts' misery with 15 minutes left to play, as Claudio Pizarro's overhead kick from a rebound left the final score at 4-1.