Newly signed Travis Zajac also provided a score as the Devils opened their defense of the Eastern Conference crown with a victory.
Martin Brodeur made 18 saves for New Jersey, which is coming off a run to the 2012 Stanley Cup finals, where they lost to the Los Angeles Kings in six games.
The Islanders got their only tally from Travis Hamonic.
Evgeni Nabokov recorded 26 saves for New York, which finished in last place in the Atlantic Division in 2011-12.
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