After a bright start from the hosts, Mario Mandzukic put Bayern ahead in the 18th minute.
After two injury-enforced alterations Nurnberg lost their shape and Bayern took control of the game, going close numerous times to making it two before Philipp Lahm sealed victory number 18 of the season on the hour mark.
Bayer Leverkusen remain second but third-placed Borussia Dortmund responded well to their fellow Champions League chasers' Friday evening win over Borussia Monchengladbach.
An emphatic 5-1 win at Werder Bremen kept up Dortmund's pursuit and left the northern Germany side in serious relegation danger.
Robert Lewandowski put Jurgen Klopp's men in front in the 26th minute before Henrikh Mkhitaryan made it two before the break.
Defender Manuel Friedrich added a third just after the break and both Mkhitaryan and Lewandowski scored again before Levent Aycicek grabbed a consolation.
Wolfsburg and Hertha Berlin both won to join Gladbach and Schalke in the chase for European places.
Wolfsburg got back to winning ways in style with a 3-0 win over Mainz, who they left three points in their wake in the standings.
Ricardo Rodriguez scored the first from the penalty spot before Bas Dost added a second. Luiz Gustavo made it three to reinforce the Wolves' place inside the top six.
Hertha added to Hamburg's plight with a 3-0 thrashing at the HSV-Arena.
After missing a penalty, Adrian Ramos scored twice while Sami Allagui was also on target as the visitors completed the job within the first 45 minutes.
Hamburg, who have the worst defensive record in the division, have now lost six games in a row and are two points adrift of safety, second from the foot of the Bundesliga.
Eintracht Frankfurt lifted themselves away from the bottom three of the Bundesliga with three first-half goals enough to see off the challenge of Eintracht Braunschweig and leave them rooted to the foot of the table.
Johannes Flum got things going for Armin Veh's men in the seventh minute before two quick-fire goals from Alexander Meier and Stefan Aigner sealed a 3-0 victory before the break.
Baden-Wurttemberg strugglers Freiburg and Hoffenheim took a point apiece from a tense 1-1 derby encounter at the Dreisamstadion.
Jonathan Schmid gave the hosts the lead midway through the first half, but substitute Anthony Modeste levelled five minutes from time.