The hosts were powerless at the Imtech Arena, allowing the away side to correct their recent defeat and strengthen their position at the top of the table
Goals from Bastian Schweinsteiger, Thomas Muller and Toni Kroos wrapped up the three points for Jupp Heynckes men, in what has been a perfect weekend for the Munich side.
After a closely contested opening, with its fair share of mistimed challenges and corners, Hamburg was the first team to carve out a respectable chance in the 13th minute.
Rafael Van der Vaart almost caught out Manuel Neuer at his front post with a first time strike, but Dante unknowingly blocked the effort, deflecting it out for a corner. Tomas Rincon struck a powerful 30-yard drive from the resulting set piece, which whistled past Bayern's post.
David Alaba and Franck Ribery were at the heart of the away side's creativity, as Bayern almost exclusively used its left flank to exploit Dennis Diekmeier.
The young fullback was responsible for Bayern's first shot on target, and provided service for an isolated Mario Mandzukic, while Ribery's drove at his marker throughout the first half and enjoyed great success.
Between its 13th minute flurry of action and the halftime whistle, Hamburg failed to create any chances, and Bayern's domination came to fruition in the 39th minute.
Kroos rounded Rene Adler, after a quick break from the away side, and looked to have wasted the opportunity to score, having taken the ball extremely wide. Instead of firing an effort at goal from a narrow angle, the midfielder chose to take his time and picked out a great cross to find Schweinsteiger at the back post, who threw himself at the ball to nod his side into a deserved halftime lead.
Hamburg boss Thorsten Fink threw on Artoms Rudnecvs at the interval to try and change the momentum of the game, but Bayern continued in the same vein as the first, with Mario Mandzukic spurning a great chance to double its lead in the 46th minute, as Adler saved brilliantly to deny the Croatian.
Muller made no mistake a minute later, however, with a phenomenal finish. The Germany international took a poor touch and raced to prevent the ball from going out for a goal kick, but then turned quickly and curled a breathtaking effort just inside Adler's back post from a seemingly impossible angle.
In the 53rd minute, Bayern was celebrating again, as Hamburg began to implode. After a delicate through ball from Ribery, Kroos hammered an effort into the roof of the net from close range, leaving Adler no chance and his side a lot to do to turn the game around.
Although the Rothosen saw more of the ball in the second half, chances were scarce, and a long-range strike from Van der Vaart was Neuer's only real save of note in a forgettable game for the home side.
A disappointing performance for Fink's side, which stays eighth, as Bayern goes well clear of second-placed Schalke.