Sergei Brylin and Patrik Elias also scored for the Atlantic Division leaders, who have won four of their last five. Trent Hunter, Andy Hilbert and Mike Sillinger scored for the Islanders, who are mired in a season-worst losing streak of five games.
Parise and Brylin scored 15 seconds apart to stake the Devils to a 2-0 lead early in the game. Travis Zajac forced a turnover in the Islanders zone and fed the puck to the slot where Parise beat Rick DiPietro with a backhander at 1:57. Brylin, set up by Jay Pandolfo, immediately followed with a goal.
The Islanders quickly countered with Hunter's goal - the third in one minute. 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.
Elias widened the Devils lead to 4-1 at 4:10 of the second by scoring from a sharp angle at the bottom of the right circle.
Hilbert connected at 11:09 when he split the Devils defence 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.
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 on a power play.
Notes: Devils defenceman Colin White missed a fifth straight game with a groin injury . . . Freddy Meyer has yet to play for the Islanders. The defenceman, 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 defenceman Johnny Oduya suffered an upper-body injury on his first shift and did not return.