Nielsen went first in the tiebreaker, lifting a high shot past Philadelphia goalie Ilya Bryzgalov after faking a backhander.
Nabokov then sealed the victory with a stop on Wayne Simmonds and the Islanders had their third win in four games.
Nabokov turned aside 45 shots in regulation and overtime, registering his second shutout of the year and 52nd of his career.
Philadelphia dropped a third straight for the first time this season despite getting a shutout from Bryzgalov -- his second whitewash of the season and 25th of his career.
Celebrity Couples of 2014 [PHOTOS]