Zubrus set up Ilya Kovalchuk's goal in the first period and scored along with Brian Rolston in the second to give the Devils a seemingly comfortable 3-0 lead.
Ryan Callahan and Vinny Prospal, in his season debut after recovering from offseason knee surgery, got the Rangers close, but Martin Brodeur hung on for the Devils (18-30-3), who moved one point ahead of Edmonton and tied the New York Islanders in the overall standings. Brodeur made 25 saves for New Jersey, 8-1-1 in its past 10.
The Devils, outshot 27-18, lost the first three meetings this season to New York and were outscored 9-2.
New York defenseman Dan Girardi nearly tied it with 0.8 seconds left, but his shot hit the right post.
Prospal brought the Rangers within 3-2 by scoring during New York's 5-on-3 power play 2:21 into the third period. Starting goalie Henrik Lundqvist was chased in favor of Martin Biron in the second after allowing three goals on only 12 shots.
New York had a pair of failed power plays after the two-man advantage in the third.
Kovalchuk connected on New Jersey's first shot to give the Devils the lead 1:04 in. Zubrus dropped the puck in the right circle to Kovalchuk for a hard shot that caromed in off the post. The assist was Zubrus' 300th in the NHL.
The rest of the opening period was relatively uneventful until the final minute when Brandon Dubinsky fired a shot toward a vacated Devils net, but struck the crossbar with 22 seconds remaining.
The teams combined for only 12 shots in the period - seven for the Rangers.
Lundqvist faced little action and appeared to be a bit shaky on the few shots that came his way. He was rattled midway through the first when he gloved another hard drive by Kovalchuk that seemed to sting his catching hand. Lundqvist was checked briefly by the trainer and remained in the game - but not for too much longer.
The Devils continued to show how they are making a second-half surge after one of the worst starts in team history and stretched their lead to 3-0.
Zubrus finished off the next scoring play, with help from defenseman Henrik Tallinder, who fed the puck to him in the high slot for a sizzling drive that Lundqvist initially stopped. The puck got behind him and trickled tantalizingly toward the goal line.
Girardi tried to sweep the puck safely out of the crease, but instead knocked it off Lundqvist and into the net at 8:01.
New Jersey got more assistance from the Rangers and turned it into another goal 7:03 later. New York forward Mats Zuccarello failed to clear the puck out of the zone, and Devils All-Star Patrik Elias deftly turned that into instant offense.
Elias curled with the puck at the blue line and sent a soft pass to his right to Rolston, who showed off his powerful slap shot and ripped a high drive past Lundqvist.
The Rangers' goalie was left sitting in the crease. When he got up, he was summoned to the bench and replaced by Biron. New York showed some life after the change and got on the board with Callahan's 12th of the season.
In his second game after missing 19 because of a broken hand, Callahan took a pass from Artem Anisimov and fired a shot from the bottom of the right circle that beat Brodeur over the left shoulder to make it 3-1 with 3:35 left in the second.
Callahan netted the tying goal Tuesday in the third period of a 4-3 shootout loss to Pittsburgh in his return.
Notes: Brodeur has played 1,029 complete games, the same number of total appearances Patrick Roy made. ... The Rangers sent C Kris Newbury to Connecticut of the AHL. ... The Devils failed to score on a two-man advantage that lasted 40 seconds in the first period.