The Devils won for the third time in four games, getting 29 saves from Martin Brodeur.
Kovalchuk produced the first two goals of the contest midway through the opening period and early in the second. His final goal of the game -- his 29th of the season -- came 8:09 into the third and gave the Devils a 4-1 lead.
The only New York goal, by Andrew MacDonald late in the second period, briefly cut the Islanders' deficit to 2-1.
Evgeni Nabokov allowed all five New Jersey goals on just 20 shots.
This was the second of three meetings these teams will have this week. The Islanders posted a 1-0 victory last Sunday and they will play again Saturday on Long Island.
Celebrity Couples of 2014 [PHOTOS]