Nabokov turned aside all 10 shots he faced in the third period with the Islanders clinging to a 1-0 lead, and backstopped New York to its first victory in four games.
Andrew McDonald scored on a first-period power play while John Tavares and Casey Cizikas each added an empty-netter for the Isles, who came into the contest three points out of the eighth and final Eastern Conference playoff spot.
Florida's Jacob Markstrom yielded just one goal on 35 shots for the Panthers, who lost for the eighth time in 10 games.
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