"Bergie had a good game. We're all so excited for him," said Isles forward Kyle Okposo of Bergenheim's milestone.
Jeff Tambellini, Okposo, Radek Martinek and Blake Comeau also lit the lamp for the Islanders, who have won three of their last four and set a season-high in goals scored.
Joey MacDonald stopped 35 shots for the win.
Brian Gionta, Jamie Langenbrunner and Patrik Elias scored for the Devils, who saw their four-game win streak halted and fell to eight points behind conference-leading Boston after the Bruins won earlier Saturday.
Martin Brodeur took the loss, allowing six goals on 26 shots through the first two periods, and remains three wins away from tying Patrick Roy for the all- time win mark.
"I knew it wasn't going to be all rosy," Brodeur said of his first loss since returning to action. "If people expect me to go out and win every single game and shut down everybody, it's not something that's gonna happen."
Kevin Weekes finished the contest by stopping the only shot he faced in the final 20 minutes.
New York blitzed the visitors with a three-goal first period and never relinquished control.
Martinek got things going just 1:42 into the contest, followed by Okposo's tip of a Josh Bailey shot at 10:59 for a power-play score.
The burst was capped when Tambellini slipped up the middle with a long lead pass by Mark Streit and beat Brodeur through the pads with a backhand at 14:05.
Gionta managed to tip a Colin White offering home 29 seconds into the second period, but Bergenheim restored the three-goal edge at 1:40.
Langenbrunner beat McDonald from a sharp angle for a 4-2 game at 4:01, but Comeau answered on the power play at the 13-minute mark. Bergenheim struck again on a screened wrister with 2:40 left in the period and the Isles took a 6-2 lead to intermission.
Elias notched a power-play score when he tipped a Paul Martin point shot home from the slot 6:48 into the third, but New Jersey failed on two consecutive power-play chances with Weekes pulled late in the game.
Bergenheim finished off his trifecta on an empty-netter from the right wing near the boards with less than a second remaining.
"I couldn't backhand it, cause it was too far away," said Bergenheim on his dilemma which led to his final goal. "I also knew there wasn't much time to take it into the middle, so I had to shoot it."