Jordan Staal, Brett Pesce, Sebastian Aho, Andrei Svechnikov and Warren Foegele scored for the Hurricanes (3-0-1), who have won three in a row.
Teuvo Teravainen logged two assists for Carolina, which recorded three first-period goals.
Staal and Aho also each chipped in with an assist for the Hurricanes, who play their next three games on the road.
Vancouver's Sven Baertschi scored twice and recorded an assist, while Bo Harvat also scored. Alexander Edler had two assists.
Canucks rookie Elias Pettersson, who supplied five points during his first two career games, was limited to an assist.
Goalie Curtis McElhinney, who made his home debut a week after he was claimed on waivers by the Hurricanes, stopped 22 shots. He's 2-0-0 this season.
Carolina clamped down in the third period while nursing a one-goal lead for a long stretch. Vancouver managed only five shots in the period. Foegele's goal with 6:12 left stretched the margin to 5-3.
Goalie Jacob Markstrom, who has played in all three Vancouver games, made 28 saves.
The Canucks (1-2-0) have played two games of a six-game road trip.
There were seven goals scored less than 24 minutes into the game.
Staal scored after only 43 seconds elapsed as it appeared the Hurricanes were picking up where they left off two days earlier when they posted four third-period goals in an 8-5 victory against the New York Rangers.
Baertschi took advantage of a Carolina defensive breakdown to pull the Canucks even at 1-1.
Pesce's goal came when the puck made it through after his delivery from the blue line.
The Canucks scored two power-play goals in the first 3 1/2 minutes of the second period to pull within 4-3, with Svechnikov scoring in between.
A third power-play chance later in the second period was thwarted, with the Hurricanes producing a couple of short-handed chances.
(With inputs from agencies.)