Sergei Brylin and Patrik Elias also scored for the Atlantic Division-leading Devils, who have won four of their last five. With the two goals, Parise has 16 for the season-tying Elias for the team lead.
"He's given us some huge goals this year," Devils coach Claude Julien said. "He's been as consistent as any player on this team. He had a good strong start and he's been building on it. He's very impressive for a second-year player."
As an emerging offensive weapon, Parise gives the Devils better scoring balance and depth.
"We're a lot harder to check when the scoring is spread out," Parise said. "That balance is something we were missing at points last year."
"The effort is there," Islanders coach Ted Nolan said. "We're not getting any breaks. We made a turnover, it's in the net."
Parise and Brylin scored 15 seconds apart to stake the Devils to a 2-0 lead early in the first period.
Brylin, set up by Jay Pandolfo, immediately followed with a goal.
"It's not the best way to start a game," DiPietro said.
The Islanders quickly countered with Hunter's goal -- the third score in a 1-minute span. Hunter tipped Sean Hill's point shot past Brodeur at 2:57.
Parise struck again at 12:58. Taking a pass from Jamie Langenbrunner, Parise spun before flipping home the puck for the fourth two-goal game of his career.
"The backhand has become my go-to move," Parise said.
In the second, Elias widened the Devils lead to 4-1 at 4:10, scoring from a sharp angle at the bottom of the right circle.
Hilbert connected at 11:09 to keep the Islanders in the game. Hilbert split the Devils defense and whipped a backhander past Brodeur.
In the third, DiPietro came charging out almost to the blue line to prevent Parise from catching up to a rolling puck-and a shot at the hat trick.
The Islanders got the only goal of the period with 19.5 seconds remaining and DiPietro pulled for an extra attacker. Sillinger knocked in his own rebound for a power-play tally.
- Devils defenseman Colin White missed a fifth straight game with a groin injury.
- Freddy Meyer has yet to play for the Islanders. The defenseman, acquired in a trade with the Flyers on Dec. 16, has missed all 10 games since the deal with a back injury.
- Hill played in his 800th game.
- Devils defenseman Johnny Oduya suffered an upper-body injury on his first shift and did not return. His status is uncertain for New Jersey's next game on Saturday in Ottawa.