Brodeur (30-13-4) also recorded his NHL-best ninth shutout this season and the 89th of his career.
Brian Gionta and Jay Pandolfo scored for the Devils, who are 11-1-2 over the last 14 games.
Tampa Bay goalie Johan Holmqvist stopped 23 shots. The Lightning lost for just the second time in their last nine games.
Gionta put New Jersey ahead 1-0 with 50.5 seconds left in the first. He scored from just outside the crease off a pass from behind the net by Scott Gomez.
Pandolfo made it 2-0 with an empty net goal with 42.5 seconds left.