Carrier gave the Hurricanes a 4-3 lead at 14:52 of the third. Semyon Varlamov stopped Andrei Svechnikov's initial shot with his left pad, but Carrier was able to shovel in the rebound with his backhand from the edge of the crease.
Jalen Chatfield scored on an empty net at 19:09 for the 5-3 final.
Carrier, Svechnikov and Chatfield each had a goal and an assist, and Sebastian Aho had two assists for the Hurricanes (13-3-2), who were coming off a 4-1 loss at the Nashville Predators on Tuesday but have won five of six. Brandon Bussi made 23 saves.
Brayden Schenn and Victor Eklund each had a goal and an assist for the Islanders (7-6-2), who were playing their first game since a 4-0 loss to the Edmonton Oilers on Saturday. Varlamov made 34 saves.
Logan Stankoven gave the Hurricanes a 1-0 lead just 57 seconds into the first period. Jackson Blake skated between three Islanders players before dropping the puck to Stankoven, who beat Varlamov short side from the left circle.
Blake extended his point streak to an NHL career-high eight games (three goals, seven assists).
Jesperi Kotkaniemi extended Carolina’s lead to 2-0 at 3:20 of the first. He redirected Jordan Martinook's centering pass on a rush over Varlamov’s blocker from in tight.
Bussi kept it a two-goal lead by saving two breakaways from the Islanders. He first denied Anthony Duclair with his right pad at 9:08 before stopping Emil Heineman's backhand attempt with his blocker at 11:34.
Mitchell Chaffee was able to cut the lead to 2-1 at 3:40 of the second period, deflecting Matthew Schaefer's point shot from the slot.
Schenn tied it 2-2 at 5:44. He got Bussi to commit while skating down the left side before tucking the puck in at the right post on a wraparound.
Svechnikov put the Hurricanes back in front 3-2 at 6:44. His initial tap-in of Aho's backdoor pass hit the left pad of Varlamov, but Svechnikov was able to knock his own rebound into the open net.
Eklund tied the game at 3-3 at 17:13 of the second, burying a one-timer from the high slot past Bussi’s blocker.
