"I think he will be all right," DeBoer said of Kostopoulos, who did not return to the game.
The Islanders dominated the first period in taking a two-goal lead, 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 said he never saw until it was too late.
"You always want to have the lead, especially against these guys," Nielsen said. "They are really good defensive team and if you get behind, it's tough to create chances. Every time you get a lead against them, they feel a little out of their comfort zone. It was huge."
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 blue line 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.
"We had a bad second period," Nielsen said. "Way too many turnovers, and Nabby saved us. But I liked the way we came out in the third."
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.
NOTES: Devils LW Dainius Zubrus played for the first time since tearing a ligament in his left wrist in game against the Rangers on Feb. 5. He had surgery and missed 26 games. ... This was the fourth time this season Nielsen had two assists in a game. ... Nabokov has started 16 of the past 17 games for the Islanders, and 31 of 36 this season. ... New York has been either tied or ahead in the third period in 30 of 36 games this season. ... DeBoer said C Travis Zajac missed portions of the game because of the flu. ...The Islanders won the season series 3-2, although the Devils (2-2-1) got five points.