Carolina snapped a two-game skid by taking a 5-0 lead midway through the contest and getting 31 saves from Cam Ward.
Jonathan Matsumoto scored his first two goals of the season in the victory, which came in just the third Carolina home game in 12 overall outings this year. The Hurricanes were shut out in their first two home appearances.
Matsumoto gave the Hurricanes a 2-0 lead with 4:12 left in the first period and Eric Staal added a goal before the stanza was over.
Brandon Sutter and Jiri Tlusty produced goals in the second.
Rick DiPietro gave up all seven goals on 32 shots and the Islanders suffered their fifth straight setback.
Ward's bid for a shutout was ruined by Michael Grabner 2:12 into the third period.