Defending champions Bayern restored their 13-point lead at the Bundesliga summit thanks to a 2-0 derby success over to make it 12 successive league victory.
Toni Kroos, who recently rejected a contract extension, was left out by coach Pep Guardiola and Josip Drmic almost gave Nuremberg the lead early on, but Mandzukic opened the scoring on 18 minutes with an improvised finish. It was the 27-year-old striker's 12th league goal of the season.
Mandzukic then set up the second for Philipp Lahm, whose shot went through the grasp of Raphael Schafer for his first Bundesliga goal since 2010.
Dortmund moved four points behind second-placed Bayer Leverkusen by thrashing Werder Bremen 5-1 on their travels.
Robert Lewandowski broke the deadlock to end his personal goal drought in the league on 475 minutes, while Manuel Friedrich and a Henrikh Mkhitaryan double put Jurgen Klopp’s side well in command. Lewandowski's second sent him top of the Bundesliga scoring chart before substitute Levent Aycicek grabbed a consolation for Bremen.
Wolfsburg beat Mainz 3-0 to move level on points with fifth-placed Borussia Monchengladbach.
A penalty from Swiss full-back Ricardo Rodriguez put Dieter Hecking's men ahead, with Brazil midfielder Luiz Gustavo and Dutch striker Bas Dost also on target. Rodriguez has now scored four goals in his last nine league appearances.
Eintracht Frankfurt cruised to a 3-0 win over rock-bottom Eintracht Braunschweig to stride four points clear of the relegation zone and leave their visitors six points adrift of safety. Johannes Flum, Alexander Meier and Stefan Aigner got Frankfurt’s goals.
Freiburg and Hoffenheim played out a 1-1 draw in a battle of sides in the bottom half. Jonathan Schmid’s 68th-mniute goal looked to have done enough for Freiburg, but substitute Anthony Modeste got a late equaliser. The point was nevertheless enough for Freiburg to escape the relegation zone.
Elsewhere, Hamburg's dreadful run continued following a 3-0 defeat at home to Hertha Berlin, their sixth successive Bundesliga loss.
The visitors should have been in front after 15 minutes when Adrian Ramos saw his penalty saved by Rene Adler, but it mattered little as Hertha raced into a three-goal lead before the break.
Sami Allagui put Hertha ahead shortly after the penalty miss before Ramos atoned for his error by scoring in the 23rd and 38th minutes to consign Hamburg to another miserable defeat, one which leaves them in the bottom two.
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