With the victory, the Islanders moved past the idle New York Rangers into the eighth and final Eastern Conference playoff spot.
The Islanders (18-16-3) have 11 games remaining while the Rangers have 13.
Both the Islanders and New Jersey Devils have 39 points. The Rangers have 37.
Nielsen's power-play goal at 19:32 of the second period came when a rebound of a Mark Streit slap shot ricocheted to him in the right circle. Nielsen fired the puck past Ondrej Pavelec for this fourth of the season.