Nielsen assisted on Josh Bailey's tally 52 seconds into the game and on a Travis Hamonic marker less than 7 minutes later, and the Islanders were never headed after that.
John Tavares added his 22nd of the season for New York, which remained knotted with the crosstown rival New York Rangers for the eighth and final playoff seed in the Eastern Conference.
Evgeni Nabokov earned the victory with 24 saves as the Isles notched their fourth win five games.
Newt Gingrich fires back at Mandela backlash
Campus cop fatally shoots Texas student during traffic stop