Pep Guardiola had demanded more from the Bundesliga champions prior to Saturday's game, after they had begun 2015 in uncharacteristically inconsistent fashion.
And Bayern responded in style, as they once again hammered Hamburg - opponents they put nine past in the corresponding fixture two seasons ago - with Robben and Muller to the fore.
Robben added his second two minutes after the restart - his 14th goal in 17 Bundesliga appearances this season - before Robert Lewandowski and Muller made it six before the hour.
It did not take long for the hosts' intense pressing to force an error in the Hamburg defence, but Jaroslav Drobny did well to deny Muller after Robben's incisive pass in the fourth minute.
Rafinha, making his first appearance of 2015 following an ankle injury, saw his cross strike the arm of Ronny Marcos and Muller coolly swept home the resulting penalty.
It took Bayern just two minutes to extend their lead, Gotze smashing in from close range after Drobny failed to hold on to Muller's powerful drive.
Hamburg had no answer to Bayern's frontline and Lewandowski added the sixth a minute after, tapping in from close range following Muller's squared pass.
Guardiola then introduced Ribery for his first taste of action in 2015 and it took the Frenchman just 10 minutes to make his mark, pouncing on a rebound and slotting in from close range.
