Sabourin, who entered the game with a 1.66 goals-against average and a .935 save percentage, was yanked after surrendering three goals on 14 shots.
Curry, making his NHL debut, stopped the 11 shots he faced.
New York's Trent Hunter had a goal and an assist.
Doug Weight and Bill Guerin also scored, while Joey MacDonald made 25 saves on 29 shots for the Islanders, who had a two-game win streak snapped.
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