Brodeur, who also blanked the Islanders 2-0 on Dec. 30 and Feb. 8, was sharp one night after allowing five goals on 24 shots in a loss to Pittsburgh. He shows no sign of slowing down, despite making 29 straight starts for New Jersey.
He has earned all of New Jersey's 36 victories this season and kept the Devils from having their first regulation losing streak since a three-game skid in December. Brodeur is third in NHL history with 91 shutouts, three behind George Hainesworth and 12 in back of Terry Sawchuk.
John Madden and Sergei Brylin supplied the goals to help the Devils win for the sixth time in eight games.
Rick DiPietro made 28 saves for the Islanders, who failed to earn a point for the second time in 13 games (7-2-4).
Madden, wearing a full cage to protect his face, scored his first goal in five games when he connected with 5:39 left in the first period. In his second game back since being struck with a puck, Madden started a pretty tic-tac-toe play that resulted in his ninth this season.
Erik Rasmussen finished it by finding Madden streaking down toward the left post for an easy redirect into the open side past DiPietro.
The lead grew to 2-0 while the Devils enjoyed a second-period power play that was created when DiPietro fired the puck over the glass.
Patrik Elias slid a pass to Brylin at the right post. DiPietro flashed his pad out to stop the shot, but Brylin corralled the rebound, waited and calmly lifted it in at 12:26.
It didn't take long for the Islanders to show their frustration against the Devils, the last team to beat them in regulation four games earlier in New Jersey.
Arron Asham dropped his gloves to fight Cam Janssen just 3:12 in as the two engaged in a long, spirited brawl that lasted until the combatants tired themselves out.
Asham got entangled with Mark Fraser in the second period and looked ready to brawl again, but teammate Chris Simon charged in to do the fighting for him. That came 3½ minutes after Drew Fata, playing his second game this season in place of injured defenceman Bruno Gervais, fought Mike Rupp.
New York registered plenty of points in the punching department, but again couldn't dent Brodeur.
The two-time Vezina Trophy winner rolled on his back to turn aside a shot by Randy Robitaille with his glove. Asham flubbed the puck as he tried to shoot in the rebound. He then robbed Mike Sillinger with 90 seconds left in the period, again sprawling out to make the save.
Asham also was denied when Brodeur stuck out his glove to knock his high shot away.
Notes: Devils RW Brian Gionta missed his second straight game with a groin injury. ... New Jersey D Brad Lukowich, formerly of the Islanders, played in his 500th NHL game. ... Gervais, who missed seven games in January and February with an ankle problem, aggravated the injury Thursday against Boston.