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.
Muller began the rout from the penalty spot, before Mario Gotze and a brilliant Robben strike put them 3-0 up at the break.
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.
Franck Ribery, returning from his thigh injury, came off the bench to make it 7-0, before Gotze rounded the scoring off two minutes from time as Bayern warmed up for their UEFA Champions League last-16 trip to Shakhtar Donetsk on Tuesday in perfect fashion.
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.
Robben and Muller continued to terrorise the Hamburg defence, and it was the latter who made the breakthrough from the spot in the 21st 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.
The champions were now rampant, and Robben put the result beyond doubt nine minutes before the interval.
The Dutchman cut inside in trademark fashion after a lethal Bayern counter-attack, and curled a delightful effort in off the post from 30 yards.
Bayern opened up a four-goal lead a minute after the break, as Robben cruised past Ronny and beat Drobny at the near post.
Their fifth followed swiftly, Muller doubling his tally for the day with a sumptuous effort from 25 yards, curling it into the bottom-right corner.
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.
And Gotze was on hand to join Robben and Muller with a brace in the game as Bayern posted yet another thrashing of Hamburg.
