Deslauriers cut it to 2-1 at 10:39, redirecting a point shot from Tony DeAngelo.
"I thought we had good opportunities when it was 2-0 to make it 3-0, and we didn't capitalize on it," New York coach Lane Lambert said. "Then they scored one. At the end of the day, it's the scoreboard that counts, and I thought we did a really good job of defending, especially toward the end."
Scott Laughton had a chance to tie it at 5:36 of the third period after skating around Islanders defenseman Scott Mayfield, but his shot from the edge of the right circle was gloved by Varlamov.
"We've played them a lot over the years here," Hart said. "They've got a lot of returning guys from over the years. They play a hard game. They play to their system really well, and that works for them, but tight game tonight."
NOTES:Palmieri has six points (one goal, five assists) on a five-game point streak. … Dobson and Islanders forward Hudson Fasching each returned from a lower-body injury. Dobson, who missed four games, had one assist in 16:34 of ice time. Fasching, who missed six games, had one shot and one hit in 9:13.