After Nielsen beat Brian Elliott in the third round of the tiebreaker, Islanders netminder Nathan Lawson secured the victory with a save on Bobby Butler, handing New York its season-high fourth straight win.
Lawson stopped 28-of-31 shots to notch his first career NHL victory in his fifth start.
Butler and Ryan Shannon scored and Elliott turned aside 25-of-28 shots for the Senators.
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