Travis Zajac scored early in the second period, and Jay Pandolfo and Brian Gionta added insurance goals late in the third.
Brodeur earned his fifth shutout this season and moved into sole possession of third place on the career list, one ahead of Glenn Hall.
The win was only the third in eight games for the Atlantic Division-leading Devils, who ended a three-game losing streak on home ice.
It was a frustrating night for Sidney Crosby and the Penguins. The NHL's leading scorer had his 10-game point streak snapped as Pittsburgh lost its fourth straight.
Zajac staked the Devils to a 1-0 lead at 1:23 of the second on a nice puck-control rush by his line. Zajac, Jamie Langenbrunner and Zach Parise crisscrossed in the Penguins zone with Zajac winding up with the puck in the right circle for a shot that beat Marc-Andre Fleury.
The assist was Langenbrunner's 100th with the Devils.