Brodeur made 26 saves to record his second straight shutout, and the Devils scored three power-play goals in the third period for a 3-0 win at Continental Airlines Arena in the Meadowlands.
New Jersey (21-18-5) now has its first five-game winning streak of the season, outscoring opponents 17-6 during the span.
"The rules are there and there is a lot more flow to the game," Brodeur said. "If we are able to play this way and not take a lot of penalties, you'll see this more and more from our team. It's not just me. All the guys are excited that we are able to shut down good teams."
New Jersey's Scott Gomez corrals the puck while Vancouver's Anson Carter gives chase during Friday's game. (AP/Bill Kostroun)
All three of Brodeur's shutouts have come in the last five games. The 33-year-old has 78 shutouts in his career.
Brian Gionta scored two goals for the Devils, with Viktor Kozlov opening the scoring. Brian Rafalski had two assists, while Scott Gomez extended his point streak to eight with an assist.
"We're beating good teams now and we're starting to roll," Gionta said. "We're playing the hockey we know how to play. We're getting back to the Devil way."
Alex Auld gave up two goals on 25 shots for the Canucks, who were trying to establish a four-game winning streak.
Vancouver (24-15-5) had won four straight games against the Devils, including the last three in New Jersey.
The Canucks failed to make ground in the jam-packed Northwest Division, remaining tied with Edmonton and Colorado at 53 points. Calgary leads the division with 55 points.
"Once they scored on the power play, I don't think we mounted much after that," Canucks coach Marc Crawford said. "We were playing a stingy road game and I thought we'd rise to the challenge of the third period, but that first goal seemed to take all the wind out of our sails."
After a scoreless first two periods, the Canucks got into penalty trouble in the third.
With Ryan Kesler off for holding, Kozlov skated from the corner to the left faceoff circle, firing a wrist shot past Auld for his 10th goal of the season at 2:31.
Just over four minutes later, with Brendan Morrison in the box for hooking, Gomez set up shop from behind the net and found Gionta, who beat defenceman Bryan Allen to the net and fired a shot past Auld.
Gomez now has eight goals and nine assists in his last eight games.
Gionta later outskated Mattias Ohlund for the puck to score an empty-net goal with less than two minutes remaining.
New Jersey went 3-for-4 on the power play, with Gionta at a career-best and counting 25 goals.
Brodeur and his teammates struggled on and off the ice earlier in the season. The departures of longtime Devils Scott Niedermayer and Scott Stevens on the blueline left a huge void, with the signings of Dan McGillis, Vladimir Malakhov and Alexander Mogilny not panning out.
As well, coach Larry Robinson resigned citing stress and family reasons, temporarily replaced by general manager Lou Lamoriello.
The team's current streak has co-incided with the return of offensive sparkplug Patrik Elias, who had missed the entire season up to that point after contracting hepatitis last spring.
While the Devils were beating Vancouver, Mogilny was playing his first-ever minor league game, with the team's AHL affiliate in Albany.
The Canucks had a power-play opportunity in each of the periods, but were denied.
"When you get a chance against that team, you have to score," Canucks forward Todd Bertuzzi said. "You're not going to get many. They are very sound defensively."
Vancouver will continue their road trip with a game Saturday against the New York Islanders, before finishing it on Monday against Pittsburgh.
