Making only his second career start in net, Nilsson turned aside all 24 shots he saw, including 12 in the third period as the Devils desperately tried for the equalizer.
The 21-year-old Swede is a third-round 2009 Islanders draft choice.
Kyle Okposo scored the game's only goal early in the second period and New York broke a three-game home losing streak to New Jersey.
Martin Brodeur was saddled with the hard-luck loss, stopping 24-of-25 shots for the Devils, who came into the contest seeded sixth in the Eastern Conference.
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