Enstrom's first goal this season broke a 3-3 deadlock at 11:29 of the final period and, with two assists, he recorded his first three-point contest this season.
New York got a goal and an assist from both Frans Nielsen and Trent Hunter.
Jon Sim also scored once, and goalie Joey McDonald, playing in place the injured Rick DiPietro, was beaten four times on 27 shots in the Islanders' seventh loss in their last nine contests.
Atlanta's Mathieu Schneider (hip) also missed the game.
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