Tlusty netted his first goal 1:05 into the second, jamming a loose puck past Evgeni Nabokov. Jordan Staal added his first with a wrist shot from the left circle at 6:36, and Jeff Skinner made it 3-0 at 13:37 with his third. He leads the Hurricanes (4-2-3) with nine points.
Matt Moulson broke through for the Islanders with his third of the season on the power play with 1:07 left in the second. John Tavares assisted, giving him a seven-game point streak. The Islanders captain has four goals and six assists during the streak.
Tlusty scored his second of the game 11:06 into the third, finishing a 2-on-1 break with Alexander Semin.
New York's Frans Nielsen scored his fourth on a power play at 13:19 of the third before Kyle Okposo made it 4-3 with 1:01 left.
The Islanders (3-3-2) sustained their first regulation loss in five home games. New York had posted two wins and two shootout losses at Nassau Coliseum.
Carolina won all three meetings last season from the Islanders, who are now their division rival. The Hurricanes are 21-5-5 in their last 31 games against New York and 10-1-2 in their past 13 visits to Long Island.
The Islanders were forced to play with five defensemen after veteran Lubomir Visnovsky was knocked out of the game with five minutes left in the first period. The team said he sustained a concussion after absorbing a hard hit.
The Islanders had another scare with just over nine minutes left the second when Nabokov collided with sliding teammate Matt Carkner in the crease. Nabokov was face down for several minutes, and was attended to by a trainer before he slowly got to his feet and stayed in the game.
NOTES: Hurricanes defenseman Ron Hainsey played his 600th NHL game. ... Carolina was without injured goalie Anton Khudobin (lower body), forward Elias Lindholm (upper body) and defensemen Tim Gleason (concussion) and Joni Pitkanen (heel surgery). ... Long Island native Mike Komisarek played his second game for the Hurricanes. The 31-year-old defenseman previously played for Montreal and Toronto.