The Frenchman burst down the left, cut inside his marker and scored with a shot inside the near post in the 78th minute, only his third Bundesliga goal of an injury-plagued season.
The win moved Bayern onto 52 points from 24 games and took them two ahead of previous leaders Bayer Leverkusen, who were held 0-0 at home by Cologne on Saturday and lost top spot despite being unbeaten after 24 games.
Hanover 96 finished the weekend in the relegation zone after they lost 1-0 at home to champions VfL Wolfsburg in Sunday's other game.
"It was an even match, Hamburg have very good players but a single player decided the match," said Bayern coach Louis van Gaal.
"I find it unbelievable that a team which hasn't lost does not lead the table but that says something about us," added the charismatic Dutchman.
The hosts made a lively start with Arjen Robben's runs down the right continually troubling the visitors. Mark van Bommel had a shot deflected wide and Thomas Mueller forced Frank Rost into a difficult save from a narrow angle in the first half hour.
Robben's runs became increasingly unproductive and predictable and Bayern's final passes repeatedly went astray.
