Dutchman was involved in three goals in the first half as Bavarians poured misery upon HSV
Daniel Van Buyten was given a surprise start in central defence ahead of Jerome Boateng, but the Belgian justified his inclusion on 13 minutes as he nodded in the opener.
Four minutes later, Thomas Muller fired a dangerous ball across the face of goal to Franck Ribery, who skillfully made space before doubling the hosts' advantage with a well-taken strike.
Robben poured the misery upon HSV as he made it 3-0 shortly after the half-hour mark. The Dutchman went on a superb solo run before chipping a gorgeous finish into the net.
Bayern's lead could easily have been even greater at half-time, but Thomas Muller had a well-taken volley rattle the post, and was denied at the last moment after sprinting into a one-on-one situation with goalkeeper Jaroslav Drobny.
Robben and Gomez also had a close call each, but were both denied by the HSV goalkeeper.
By contrast, Hamburg very rarely ventured out of their own half, and their only real chance of the first half came on 29 minutes as Dennis Diekmeier surged forward and had his low drive parried by Manuel Neuer.
After the break, Ribery had a long-ranged shot parried before an unmarked Muller missed from just inside the penalty area. Hamburg were woefully deficient in attack and sorely missed the influence of injured forward Mladen Petric.
Bayern did not let up after the break, and on 57 minutes, Mario Gomez finished from a tight angle, his first goal from free play this season.
The pace of the game slowed after Gomez's goal, but following the introduction of a number of substitutes, Ivica Olic saw a header saved moments before he nodded in the fifth.
The result ses Bayern advance to second in the Bundesliga, one point behind Monchengladbach, and ahead of six other teams on goal difference. Hamburg are 17th, having earned just a single point from three matches.