Zach Parise and Dainius Zubrus also had a goal and an assist each for the Devils, who improved to 2-1 so far on their six-game road trip. Brian Rolston and Brian Gionta also scored, while Scott Clemmensen made 26 saves in the win.
Alex Burrows, Steve Bernier and Pavol Demitra had the goals for Vancouver, which has dropped three consecutive contests. Jason LaBarbera gave up two goals on six shots in the start for the Canucks, and was replaced by Curtis Sanford, who made 19 saves the rest of the way.
New Jersey led by two to start the third period, and seemed to have the game in hand after scoring shortly into the frame. Zajac skated on the left side of the ice on a rush and dished the puck to Jamie Langenbrunner, who sent the puck immediately back to Zajac for the one-timer past Sanford at 4:19.
But despite trailing 4-1, the Canucks got back in the game with two goals later in the third. Demitra stuffed in a rebound with 7:41 remaining, and five minutes after that goal, Bernier swatted at a loose puck at the left side of the goal line. The narrow-angle shot sneaked past Clemmensen, bringing the suddenly energized hosts within 4-3.
Vancouver peppered Clemmensen with shots over the next several minutes, throwing the puck on net from every direction and managing to keep it in the offensive zone.
But after emptying the net in the final minutes, New Jersey managed to clear the puck, sending the Canucks back on defense and forcing an end to the surge. With under a minute remaining, Patrik Elias attained the disc on the right side of the ice in the neutral zone and passed the puck to Zubrus on the left. Zubrus' shot from there hit off a Vancouver stick and went into the net with 39 ticks left, and the Devils held on for the win.
New Jersey scored three times in the first period to take a commanding lead. Rolston tallied at 1:05, and at 3:29 Parise netted his 25th of the season, ending LaBarbera's outing. Gionta got one past Sanford a little past the midway point of the opening period, and the Devils led 3-0 going into the second.
Burrows got Vancouver on the board at 11:01 of the middle frame when he one- timed a sharp rebound off Clemmensen's pads back into the net, and the Canucks trailed 3-1 going into the second intermission.