The game was scoreless until Bernier scored on a power play with 3:54 left in the final frame, then followed that up with another tally a little more than 1 minute later to seal the victory.
Hedberg, meanwhile, turned aside all 22 shots he saw to notch his first shutout of the year and 22nd of his career as New Jersey rebounded from a Saturday loss to Pittsburgh.
Evgeni Nabokov stopped 24-of-26 shots for the Islanders, whose two-game winning streak was snapped.
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