Jamie Langenbrunner and Patrik Elias also scored for the Devils, who opened their season with an easy win in the arena where their playoff run ended last season. Martin Brodeur made 29 saves for his 81st career shutout.
Cam Ward finished with 26 saves for the Hurricanes, who were outplayed in the first period and never recovered.
It was a frustrating performance for Carolina in a game billed as "Opening Night 2," designed to be a smaller-scale Cup celebration for fans who couldn't get a ticket to Wednesday's opener against Buffalo. It included a brief pregame video montage of last year's playoff run on the scoreboard, as well as a spotlighted appearance by the 114-year-old Cup.
Last season, Carolina won its first seven home games en route to a franchise-record 31 wins at the RBC Center. The Hurricanes then beat the Devils in the Eastern Conference semifinals, ending it with a 4-1 win at Carolina on May 14.
But the Devils looked sharp in their return Friday, getting Parise's first goal 26 seconds in and never looking back.
Parise scored when he tipped in a shot from Colin White at the blue-line, the first of three redirections that slipped past Ward.
Langenbrunner followed with a score at 11:30 of the first period, while Elias redirected a shot from Gomez at 17:32 to cap a dominating period.
Parise scored again in the second, getting a step on Ray Whitney as he cut to the crease to take a cross-ice pass from Gomez. Parise knocked the airborne puck just inside the left post at 6:01, giving New Jersey a 4-0 lead that stood up after video review.
Notes: Carolina's Peter Laviolette coached in his 300th NHL game. . . . The teams have met in each of Carolina's last three appearances in the playoffs. The Devils won a first-round series in 2001, while the Hurricanes won in the first round in '02 and the second round last season en route to the Cup finals in both years. . . . New Jersey outshot Carolina 20-8 in the opening 28 minutes before finishing with the 30-29 shot advantage.