Parise and Scott Gomez staked the Devils to a 2-0 lead and David Clarkson added a third-period, power-play goal against backup goalie Mike Dunham, who subbed for injured Rick DiPietro. DiPietro sat out because of headaches first felt following Sunday's overtime loss to the New York Rangers.
While the Devils are back in the post-season, the Islanders' chances took a double hit. They entered the night in a three-way tie for eighth place in the Eastern Conference - the playoff cutoff - but have only six games remaining and no idea if DiPietro will be back in time to help them.
New Jersey has no such goalie issues and won its second straight after dropping four of five. Brodeur made 23 saves and beat the Islanders for the sixth time this season, including three shutouts. He is three wins shy of tying Bernie Parent's NHL record of 47 victories in a season.
The Devils remained tied with Pittsburgh atop the Atlantic Division.
Alexei Yashin's power-play goal got New York within 2-1 in the second period and Jason Blake scored his 38th goal to make it 3-2 with 6:21 left in the game.
Dunham was better than in three appearances after DiPietro injured his head on March 13, but not as sharp as DiPietro has been. Dunham finished with 29 saves on 32 shots, and was replaced by Wade Dubielewicz 6:35 into the third because of leg cramps.
DiPietro is in the first season of a landmark 15-year contract with the Islanders. He left in the first period against the Canadiens two weeks ago following a mid-ice collision with Montreal forward Steve Begin. Dunham relieved and allowed five goals on 32 shots in the loss.
Dunham also played the next two games, giving up 11 goals on 61 shots in losses to Ottawa and Florida. DiPietro went 2-0-2 in four games after returning.