That was just the cushion New York needed to improve to 5-0, matching the team's best start established in 1983.
The excitement of the latest victory was tempered following the death of 19-year-old Rangers prospect Alexei Cherepanov, who died earlier Monday while playing a game in Russia. Cherepanov collapsed on the Avangard Omsk bench while talking to teammate and former Rangers captain Jaromir Jagr.
John Madden got the Devils within 2-1 late in the second period, but New Jersey continued to struggle with the Rangers, who knocked them out of the first round of last season's playoffs in five games.
New York went 7-0-1 against the cross-river rival Devils (2-1) last season.
Henrik Lundqvist was sharp after getting the night off in the Rangers' 4-3 victory at Philadelphia on Saturday, and had 25 saves in going to 4-0.
Brodeur stopped 20 shots in making his 44th consecutive regular-season start, but remained 11 wins behind Patrick Roy's NHL record for career victories.
A rare error by Brodeur, the reigning Vezina Trophy winner, gave the Rangers a 1-0 lead with 6:30 left in the first period.
Dubinsky fired a drive that clipped the stick of Devils defenseman Johnny Oduya, who was guarding him, and fluttered toward Brodeur. The goalie tracked the shot after the deflection and had his glove in position to snare it, but the puck tipped off the webbing and sailed into the net.
Brodeur tossed his head back in disbelief as the jubilant Madison Square Garden crowd showered him with derisive chants of "Mar-ty, Mar-ty." And Brodeur couldn't even blame longtime nemesis Sean Avery, who left the Rangers during the offseason.
It was Avery who faced Brodeur and waved his stick in front of the goalie during the teams' playoff series last spring, leading to a rule change the following day to make that practice illegal.
New York became the first team in three games to score more than once against the workhorse Brodeur, who already has posted a pair of 2-1 victories.
By the end of the game, the chants of "Hen-rik, Hen-rik" saluted Lundqvist. Ryan Callahan made it 4-1 by scoring into an empty net with 57.9 seconds remaining.
During a power play, Voros created traffic in front of the New Jersey net and didn't move out of position even though he was shoved by big defenseman Colin White and a bit by Brodeur, who struggled to see around him.
Several shots failed to get through the maze of players, but defenseman Dan Girardi ripped a drive that Voros tipped with his stick and directed into the net 6:37 into the second.
Voros, who had a goal and assist in the Rangers' home opener on Friday, has three goals and four assists during a four-game point streak.
The Devils cut their deficit to one late in the period when Madden got to a rebound in front and swatted a backhand past Lundqvist with 1:48 left for his first goal.
Notes: The Rangers killed New Jersey's three power-play chances and are 21-for-21 this season. ... LW Dan Fritsche made his Rangers' debut, taking the spot of Patrick Rissmiller, who sat out with an ankle injury. ... Jay Pandolfo and Zach Parise both earned their first assist of the season on Madden's goal.
