Robert Lewandowski scored a hat-trick and missed a penalty as he reached 100 Bundesliga goals for Bayern in an embarrassingly one-sided match which was over as a contest after 20 minutes.
It was a sadly familiar story for Hamburg who have conceded 50 goals in their last eight Bundesliga games at Bayern, including two 6-0 defeats, two 8-0 losses and one 9-2 reverse.
Leaders Bayern stayed 20 points clear of Schalke 04, who won 1-0 at Mainz 05 on Friday, with eight games to go and are only two wins away from clinching the title.
Hamburg, the only ever-present team in the Bundesliga's 55-year history, will now have to pull off a great escape to keep their proud record intact. They are 17th in the 18-team table and seven points adrift of Mainz in the relegation playoff spot.
Hamburg held out for eight minutes before Gotoku Sakai's tackle on Arjen Robben succeeded only in sending the ball to the feet of Franck Ribery and the Frenchman rounded Christian Mathenia to open the scoring.
Four minutes later, Robben found Joshua Kimmich in space on the right and his cross was headed in by Lewandowski for the second.
It was all too easy for Bayern who added a third in the 19th minute. Jerome Boateng picked out David Alaba with a long pass forward and the Austrian side-footed the ball into the path of Lewandowski for the Pole to score first-time.
Robben got in on the act in the 55th minute with a left-foot shot from the edge of the area and Ribery slalomed his way through the Hamburg defence for his second and Bayern’s fifth.
Lewandowksi missed a chance for his hat-trick as he sent his penalty over in the 86th minute but he made amends when the hosts were awarded another spot-kick shortly afterwards.
Hoffenheim added to VfL Wolfsburg's problems with a 3-0 win which left their opponents in 15th place and ahead of Mainz only on goal difference.
Nico Schulz and Serge Gnabry scored for seventh-placed Hoffenheim before Joshua Guilavogui put through his own net.
Michael Gregoritsch scored twice to lead Augsburg to a 3-1 win at Hannover 96, who replied with a long-range effort from Salif Sane, while Hertha Berlin and Freiburg played out a goalless draw.
(Writing by Brian Homewood in Bern, editing by Ed Osmond)
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