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 their 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 their unbeaten run against their 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 drop into the bottom three after their seventh defeat of the season, with Freiburg moving ahead of them following a draw with Hoffenheim.
Bayern, who were without Franck Ribery following surgery, started slowly and were unfortunate not to fall behind in the opening minutes as Japanese midfielder Kiyotake clipped the crossbar with an acrobatic volley.
Nurnberg looked lively, but their profligacy in front of goal came back to haunt them as 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 and Thomas Muller should have converted the rebound, only to see his header crash against the crossbar.
Bayern were starting to exert real pressure on Nurnberg, but, moments after Mandzukic saw a header easily saved by Schafer, the hosts spurned a decent chance to level.
Substitute Tomas Pekhart, who replaced Daniel Ginczek in the 22nd minute, was unmarked on the edge of the penalty, but he fired wide after good work down the left.
Three minutes into the second half the visitors, Bayern did double their 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 throughball from Lahm, 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.