Hosts Hamburg grabbed the winner a minute before halftime when Mladen Petric headed the ball over keeper Michael Rensing.
Hamburg have 36 points and Bayern are third on 35.
Second-placed Hoffenheim and Hertha Berlin, in fourth, play on Saturday against relegation-threatened Energie Cottbus and Eintracht Frankfurt respectively.
Hamburg coach Martin Jol used speedy midfielder Jonathan Pitroipa and a well organised defence to stifle playmaker Franck Ribery's creativity in the first half.
The hosts nearly scored after six minutes when Piotr Trochowski's fierce low drive rattled the post after Rensing stretched to get his fingers to the ball.
Hamburg were lucky, however, to have a Luca Toni goal disallowed for a foul by the Italian striker on defender Bastian Reinhardt.
Petric netted the winner in the 44th minute, heading Rensing's poor clearance of David Jarolim's shot over the keeper.
"We had a very compact team tonight," Petric told reporters. "We dominated the first half and were under greater pressure in the second but we held on. This win is a great boost for us but there are tough matches ahead."
A minute into the second half Petric could have added a second but his shot hit the post before Paolo Guererro fired over the crossbar.
Bayern went on the offensive and came close in the 48th when Miroslav Klose heading a Ribery cross towards the goal and keeper Frank Rost saved on the line.
Klose and Toni missed opportunities to equalise before Bayern coach Juergen Klinsmann threw on a third striker, Landon Donovan, on loan from the Los Angeles Galaxy, to pile on the pressure.
Despite several more chances they failed to get the equaliser.
"It was a tough match," Jol said. "We had a bit of luck in the second half but overall, 1-0, I think is in order."
