Nuremberg went closest to breaking the deadlock as Bayern struggled to get their game going in the first half, though David Alaba missed a penalty for the hosts.
When Pep Guardiola's side found top gear in the second half, though, there was only one side who was going to win with wingers Ribery and Robben clinching their third straight win.
Gotze and Thiago Alcantara were included in the Bayern starting XI for the first time as Guardiola rotated his team in view of a trip to Freiburg on Tuesday and the UEFA Supercup against Chelsea on Friday.
One of Bayern's strengths last season was their ability to make seamless changes to their starting XI, but the impression was the two new recruits did not entirely have a full understanding of their roles.
Nuremberg nearly capitalised when Daniel Ginczek picked up possession in midfield, cut inside onto his right foot and sent in a powerful shot which Manuel Neuer touched onto the underside of the crossbar with his fingertips.
It was the third time in three games that Ginczek had hit the woodwork as Bayern went close to falling behind for the first time this season.
They had the chance to take a customary lead in the 33rd minute when Arjen Robben went to ground easily and a penalty was awarded. Justice was probably done when Raphael Schafer guessed right and denied Alaba, who became the second Bayern player to miss a penalty this season after Thomas Muller.
Bayern raised their game in the second half, spending nearly all of the time in the Nuremberg half.
Their pressure finally told in the 69th minute when Ribery scored a rare headed goal from Philipp Lahm's cross.
Less than 10 minutes later, Robben sealed victory with a fine individual goal.
He cut in from the right wing and beat three defenders on his way into the penalty area, where he then slotted the ball through Schafer's legs and in off the inside of the far post.
Xherdan Shaqiri should have made it three, but his shot grazed the outside of the right-hand post with the goal gaping.