It was the fourth and final meeting between the metropolitan rivals this season and the series wound up at 2-2.
Until Carcilio's game-winning goal, all of the scoring had been packed into a stretch of 40 seconds late in the first period.
Brock Nelson put the Islanders in front with 1:27 to go in the opening stanza and Benoit Pouliot tied it with 47 seconds remaining.
Carcilio's goal came 4:36 into the third period. It was his third of the season and his first in eight games.