Dutch international Robben scored one goal and set up another for Daniel van Buyten, with Franck Ribery, last season's top scorer Mario Gomez and substitute Ivica Olic also on target as the hosts kept a clean sheet for the third straight game in all competitions.
Dortmund were made to work much harder against aggressive Nuremberg and had to wait until early in the second half to celebrate when Mario Gotze in the box cut back for Robert Lewandowski to thunder in for the lead.
Kevin Grosskreutz added another for the hosts 10 minutes from time with a deflected long-range effort.
Both Bayern and Dortmund moved up to six points from three games, one behind Borussia Monchengladbach, 4-1 winners against VfL Wolfsburg on Friday.
"This was our best performance this season and when everyone hits top form we will be even better," said a beaming Bayern coach Jupp Heynckes.
"I am especially happy not only with the chances we carved out but also because we again did not concede a goal. That was not because Hamburg were weak but because we were focused, and very compact."
On a sun-drenched Munich afternoon, Robben wreaked havoc down the right wing repeatedly leaving hapless Hamburg defenders in his wake.
He picked out defender van Buyten, a surprise inclusion in the place of Jerome Boateng, with a free-kick and the Belgian paid back Heynckes' trust with a well-timed header in the 13th minute.
Bayern, fresh for their 2-0 Champions League play-off first leg win over FC Zurich in midweek, kept up the pressure and Frenchman Ribery doubled their lead four minutes later when he picked up a Thomas Muller pass, flicked the ball on to his left foot and released from 10 metres to beat keeper Jaroslav Drobny.
ROBBEN CHIP
Drobny did well to deny Bayern another goal a little later as he palmed a Gomez diving header over the bar with a reflex save but could do nothing when Robben raced past Marcell Jansen and Dennis Aogo down the right and beautifully chipped the ball over the Czech keeper.
Gomez scored his first league goal of the season 11 minutes after the restart and with Hamburg's defence in tatters, Croat Olic completed the rout 10 minutes from time. Hamburg, who had lost 6-0 in Munch last season and could have conceded even more on Saturday, are 17th with just one point.
Dortmund were far less impressive and were lucky not to have fallen a goal behind in the first half. Coach Jurgen Klopp admitted his team lacked their usual offensive spark.
"Nuremberg defended very well for a long time and they also took the initiative," Klopp told reporters.
"It was a tough piece of work for us today but in no way were we lucky. We deserved to win. In the second half we created more options for us."
Fellow Champions League competitors Bayer Leverkusen also have six points following their 1-0 win at VfB Stuttgart after Stefan Kiessling made the most of Stuttgart keeper Sven Ulreich's fumble to snatch the winner,
