Elias recorded his fourth career hat trick and added two assists for a career-high five points, helping New Jersey shake off an 0-3
Arnott added two goals and two assists and Sykora collected three assists.
Elias, a 25-year-old Czech, scored 5:54 into the first period, 5 1/2 minutes after Teemu Selanne gave the Sharks a 1-0 lead. Sykora battled to keep a rebound alive behind the net and fed a pass to Elias in the crease. He banked the puck off the right goalpost to tie it.
Elias tallied twice in the Devils' four-goal second period. He weaved past defenseman Bryan Marchment and deked around goaltender Evgeni Nabokov before pushing a shot toward the vacated net. The puck started to slide away from the goal line, but Marchment skated into it, deflecting it into the net to put New Jersey up, 3-1.
Arnott got into the act just over two minutes later. He outskated defenseman Magnus Ragnarsson to a loose puck in the San Jose zone and backhanded a puck into the far corner of the net.
Elias struck again at 11:51, picking up a rebound at the right faceoff circle and lifting a shot over an out of position Nabokov.
Pierre Dagenais scored the eventual game-winner on a questionable call 55 seconds into the second period. A shot by defenseman Brian Rafalski deflected off of a stick and skipped into the air. Dagenais knocked it down and over Nabokov's shoulder.
Referees Terry Gregson and Dave Jackson had the goal reviewed to make sure Dagenais did not hit the puck with a high stick.
Arnott capped the scoring early in the third period and has four goals and four assists in five games this season.
San Jose grabbed a 1-0 lead on its first shot. Selanne skated in from the right corner and flipped a backhander over the shoulder of goalie Martin Brodeur 18 seconds into the game.
Nabokov surrendered four goals on 20 shots and was replaced by Miikka Kiprusoff eight minutes into the second period. It was the first time since March 29, 2000 the Calder Trophy winner did not complete a start.
The loss ended the Sharks' four-game unbeaten streak.