The hosts found themselves three goals ahead at the break as Muller scored from the penalty spot before Robben and Gotze wrapped up the three points before the first half had even come to an end.
The visitors appeared willing to sit on the back foot as they looked to frustrate Bayern, but Guardiola’s side were offered a chance to break the deadlock when Ronny Marcos handled inside the box.
Muller took on the responsibility to fire home from 12 yards, and the opening goal opened the floodgates as Bayern continued to pile on the pressure.
It was 2-0 to hosts less than a minute later when Drobny pushed a Muller effort into the path of Mario Gotze who kept his composure to slot in the rebound.
Hamburg were unable to offer much attacking threat as Bayern’s midfield dictated the tempo, and a third goal arrived in spectacular fashion thanks to Robben
Robben again piled the misery on the travelling supporters early in the second half by turning past Marcos in the box and beating Drobny with a low effort from a tight angle.
The onslaught was seeming unstoppable as Muller joined Robben in scoring his second with a fine strike after being gifted space on the edge of the own box.
Bayern refused to take a backward step, and a sixth goal arrived a minute later when Robben played in Muller, who crossed the ball across the six-yard box to allow Lewandowski to tap in from close range.
Franck Ribery came off the bench to score his side’s seventh with a simple finish after Lewandowski was denied by Drobny.
Hamburg were unable to relieve the pressure in the closing stages, and Gotze cashed in to complete the scoring with a fine curled effort from just inside the box in the 89th minute
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