Jerome Boateng opened the scoring after five minutes and Mario Gomez doubled Bayern's advantage in the 17th minute before Rafinha made it 3-0 after just 24 minutes.
The visitors were handed a chance to get back into the game at the start of the second half but Timmy Simons saw his penalty saved by Tom Starke, and Xherdan Shaqiri sealed the rout before the hour mark to comprehensively end Nuremberg's nine-game unbeaten run.
Bayern coach Jupp Heynckes, whose side were drawn against Barcelona in the Champions League semi-finals, made nine changes from the XI which saw off Juventus in the midweek quarter-final, with only Daniel van Buyten and Franck Ribery keeping their starting spots.
That did not affect the hosts' attacking prowess, though, and they took the lead after only five minutes when Claudio Pizarro's pass from a corner found Boateng, who hammered a volley from 12 yards into the back of the net.
Boateng set up Bayern's second goal 12 minutes later with a through-ball to Gomez, who beat Nurnberg goalkeeper Raphael Schafer at his far post with a left-footed shot.
The champions increased their lead in the 24th minute when Rafinha's effort from the right flew just inside Schafer's near post.
It was almost 4-0 two minutes later but Gomez shot over the bar from six yards out.
The visitors finally created a chance in the 44th minute but Bayern goalkeeper Starke saved Markus Feulner's attempt.
Nuremberg were awarded a penalty two minutes after the interval when Rafinha was adjudged to have fouled Mike Frantz in the box. But Starke kept out Simons' spot-kick with his head to preserve his clean sheet.
Bayern added a fourth goal in the 56th minute when a corner fell to Shaqiri, who lashed into the bottom-right corner.
Heynckes' side took their foot off the pedal at 4-0 and Nuremberg looked the more likely to score thereafter, but there were no further goals.