Bussi, who is from Sound Beach, New York, made 12 of his 28 saves in the third period.
Mark Jankowski scored the go-ahead goal late in the third period, and Nikolaj Ehlers also scored for the Hurricanes (53-22-7), who ended the regular season on a five-game point steak (4-0-1).
Bo Horvat scored his 300th career goal for the Islanders (43-34-5), who lost seven of their final eight games of the season (1-7-0). David Rittich made 19 saves.
Ehlers gave Carolina a 1-0 lead at 3:05 of the first period, breaking down the right wing and beating Rittich blocker side from the right circle. Felix Unger Sorum, who was recalled from Chicago of the American Hockey League on Monday, had the primary assist in his NHL debut.
Bussi kept it a one-goal game at 6:37, stopping Calum Ritchie twice with his left pad before stretching out his blocker to deny Matthew Schaefer from the low slot.
Rittich then returned the favor by stopping Jackson Blake on a breakaway at 15:31 of the first to keep the Islanders down just 1-0.
Horvat tied it 1-1 during a delayed penalty at 13:14 of the second period, scoring on a one-timer from the low slot off a pass from Mathew Barzal. Victor Eklund, who was recalled from Bridgeport of the AHL on Tuesday, had the secondary assist in his NHL debut.
Tony DeAngelo had a chance to give the Islanders the lead at 16:50 of the second, but Bussi sprawled out with his left pad and was able to cover up the puck in the crease.
Jankowski put Carolina in front 2-1 at 14:38 of the third period. He curled out unchecked into the bottom of the right circle and roofed a shot short side over the glove of Rittich.
