Defenceman Brad Lukowich scored in the first period, ending a 20-game goal drought with his second of the season. The surging Devils won for the ninth time in 11 games (9-1-1) and moved 10 points ahead of the second-place Rangers in the Atlantic Division standings.
Brodeur wasn't tested much in his 88th career shutout but came up big when it counted, stopping Martin Straka in front with 3:44 to play.
Before that, the Rangers' best scoring chances came in the opening minutes. Defenceman Marek Malik hit the post while coming in late on a play about five minutes into the game, and Brendan Shanahan was stopped by Brodeur on a breakaway a couple of minutes later.
Henrik Lundqvist made 31 saves the Rangers.
Lukowich's goal came on a shot from the left point with Devils forward Jamie Langenbrunner in front of Lundqvist. Langenbrunner attempted to deflect the shot, which might have caused the Rangers' goalie to miss it.
Devils forward Brian Gionta created a little excitement late in the opening period, shoving a rebound into the net with his glove, but the apparent goal was quickly waved off by the officials.