The Bavarians, who had won 10 of their 11 league games this season, paid the price for a string of big name absences and a desire by coach Jupp Heynckes to rotate ahead of next week's Champions League clash against Valencia.
Forward Mario Mandzukic confirmed his superb form with his ninth league goal in the third minute before it was Bayern's turn to be stunned, a minute after the restart with Markus Feulner's long-range effort.
"This is no disaster," Bayern coach Jupp Heynckes told reporters. "You just cannot win every game. We can live with this draw.
"We could have added another after the 1-0 but instead we conceded the equaliser at the worst possible psychological moment for us [right after the restart]."
Champions Borussia Dortmund, in fourth place, closed to within nine points after a 3-1 home victory over Greuther Fuerth, firing in three goals in the first half with Mario Gotze scoring one and setting up another for their first back-to-back league wins this season.
Schalke, however, failed to take advantage of Bayern's slip-up, slumping to a 2-0 defeat at Leverkusen.
SCHURRLE MISSILE
Germany international Andre Schurrle's 20-metre missile on the stroke of half-time and a perfect low drive by Stefan Kiessling for his eighth goal of the season made sure Leverkusen bounced back from last week's defeat by VfL Wolfsburg to remain in fifth place on 21.
Schalke, on 23 points, had defender Kyriakos Papadopoulos sent off after a second booking late in the game.
Eintracht Frankfurt joined Schalke on 23 with a 4-2 victory at home to struggling Augsburg courtesy of two Alexander Meier goals that lifted him jointly top of the scorers' list along with Bayern's Mandzukic.
Hamburg SV hauled themselves up to eighth with a 1-0 home win over Mainz 05 with Hannover 96, in sixth on goal difference, slumping to a 2-1 home defeat by Freiburg.
Eager to grab their 11th win in 12 league games, Bayern got off to a flying start with Croat Mandzukic tapping in a Toni Kroos cutback in the third minute before hosts Nuremberg's unusual 4-1-4-1 formation had any time to flourish.
Bayern coach Heynckes had to leave injured Luiz Gustavo, Franck Ribery and Arjen Robben in Munich and opted not to include Mario Gomez, back after ankle surgery in August.
Their absences were bitterly felt as Bayern enjoyed the lion's share of possession in the first half but lacked the creativity to convert it into chances.
It was Nuremberg's turn to catch Bayern cold a minute after the break with Feulner's 25-metre drive beating goalkeeper Manuel Neuer.
Timo Gebhart was sent off 14 minutes from time with a second booking after elbowing Bastian Schweinsteiger, spoiling an otherwise successful day for Nuremberg, who move up to 14th on 12 points.
