The Germany international hit his first goal in 95 games after the Croatian secured an earlier lead as Pep Guardiola's side made it 45 Bundesliga games without defeat
It took Pep Guardiola's side 15 minutes to get into its stride, but only after the defending champions survived an early scare when Hiroshi Kiyotake struck the woodwork, before Mandzukic opened the scoring with his 12th league goal of the season.
The Croatia international striker then turned provided three minutes after the break with a perfect pass to find Philipp Lahm and the midfielder fired past Raphael Schafer to end a 95-game goal drought.
Victory sees Bayern extend its unbeaten run against its Bavarian rivals to 13 games in all competitions and make it 45 games without defeat in the Bundesliga, while also extending the team's lead over Bayer Leverkusen at the top of the table.
Gertjan Verbeek's Nurnberg side drops into the bottom three after its seventh defeat of the season, with Freiburg moving ahead following a draw with Hoffenheim.
Bayern, which was without Franck Ribery following surgery, started slowly and was fortunate not to fall behind in the opening minutes as Japanese midfielder Kiyotake clipped the crossbar with an acrobatic volley.
Nurnberg looked lively, but Mandzukic opened the scoring with Bayern's first chance of the game in the 18th minute.
Mario Gotze released David Alaba down the left and he delivered a perfect cross into the six-yard box that the Croatian striker fired past Schafer, despite close attention from Marvin Plattenhardt.
Arjen Robben went close to doubling Bayern's lead with a 25-yard free kick just after the half-hour mark that struck the post with Schafer well beaten. Thomas Muller should have converted the rebound, but his header crash against the crossbar.
Three minutes into the second half, Bayern did double its lead through Lahm, with Mandzukic turning provider with a neat square pass from inside the penalty area that the Bayern captain made no mistake with from six yards.
Robben went close to adding a third in the 55th minute after a reaching a through ball from Lahm, but the Netherlands international did not fully connect with his volley and that nearly caught Schafer out at his near post.
Muller and Robben were both withdrawn from the action with the result beyond doubt as Bayern comfortably recorded an 18th league win of the season.