New York's only loss was a 2-0 setback to the Pittsburgh Penguins, the winners of 15 straight games.
Alexei Ponikarovsky scored for the Devils, who are 0-1-3 since forward Ilya Kovalchuk was sidelined with a shoulder injury more than a week ago. Martin Brodeur finished with 18 saves.
The two squared off after Martin checked Stephen Gionta and Martin caught the New Jersey tough guy right on the jaw with a right that sent him to the ice.
To his credit, Martin immediately motioned to the Devils bench for help for the dazed player.
The Islanders dominated the first period in taking a 2-0 lead in the opening 7:14 on goals by Bailey and Hamonic, while the Devils controlled the second in cutting the deficit in half on a goal by Ponikarovsky.
Nielsen had the primary assist in getting the Islanders off to a quick start against Brodeur. He made a nifty pass on a 2-on-1 break to set up Bailey's second goal in four games.
Hamonic's first goal in 19 games was a weak wrist shot from the point that Brodeur seemingly missed, or at least that's the way he reacted. While defenseman Andy Greene was in front of him, the puck didn't seem to hit him.
New Jersey, which didn't have a shot in the opening 7:25 and had only four in the first period, found its legs in the second.
Ponikarovsky snapped an 18-game goal drought by re-directing Patrik Elias' centering pass past Nabokov. Elias set up the goal by skating around Isles defenseman Mark Streit at the blueline to set up an odd-man rush.
That goal should have tied the game, but Devils' leading goal scorer David Clarkson banged a rebound off the post with the net wide open minutes earlier.
Tavares, who is second to Steven Stamkos in the NHL's goal-scoring race, gave the Islanders breathing room 9:13 into the third period with his ninth power-play goal. It was a shot into an open net after a cross-ice pass by Lubomir Visnovsky found its way through a crowd to him.