Jay Pandolfo and Brian Rafalski scored for the Devils (7-5-1), who have won three of their last four games.
Chris Higgins countered with his eighth of the season for Montreal (7-3-3), which ended a run of four games with at least one point.
Cristobal Huet made 27 saves for the Canadiens, including a glove save on a Jamie Langenbrunner breakaway in the third period.
Julien got polite applause from the sellout crowd of 21,273. He was fired after three years in Montreal last January when GM Bob Gainey opted to take over as head coach until Guy Carbonneau moved into the job this season.
The teams were each a man short when Pandolfo opened the scoring at 12:29, completing a tic-tac-toe play with Colin White and John Madden with a shot into an open side.
A puck wildly bouncing in the crease ended up on Rafalski’s stick for a power-play goal – the first allowed by Montreal’s penalty killers in 22 chances-at 10:52 of the second frame.
But Higgins got it back with the man advantage when his tip of Craig Rivet’s shot dribbled between Brodeur’s pads at 13:46.
New Jersey centre Travis Zajac missed half the first period while getting repairs after he was cut on the cheek by Guillaume Latendresse’s stick.
Alex Kovalev was helped off with a minute left in the second frame favouring his right knee, on which he had surgery last season, but he returned for the final period.
Brodeur got a scare when he was bowled over in his crease by Latendresse 13 minutes into the third period, but he was able to resume play after a visit from the trainer.
The Canadiens remain at home to face the Edmonton Oilers on Tuesday night before playing four in a row on the road. The Devils play Tuesday at home against Carolina, who they beat 4-0 in their season opener on Oct. 6.
Notes: F Scott Gomez, who suffered a groin injury this week, did not play. D Brad Lukowich (bruised foot) missed a fourth game for the Devils. D Richard Matvichuk (back), D David Hale (eye), and F Jason Wiemer (knee) are out with long-term injuries. . . . New Jersey was 4-0 against Montreal last season and last lost in the regular season to the Canadiens in March, 2004. . . . D Mathieu Dandenault (leg) and D Francis Bouillon (knee) are out long-term for Montreal.