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 Goetze 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 move up to six points from three games, one behind Borussia Moenchengladbach, 4-1 winners against VfL Wolfsburg on Friday. Champions League competitors Bayer Leverkusen also have six with a 1-0 win at VfB Stuttgart. Hamburg are 17th with only one point.
Hanover 96 and Mainz 05, also on six, take on Hertha Berlin and Schalke 04 respectively on Sunday.