Jonathan Marchessault, Reilly Smith, Paul Cotter and Brett Howden scored for the Golden Knights (40-20-6), who have won two in a row and five of their past six. Alex Pietrangelo had two assists.
"I think [Quick] is building confidence in his game," Vegas coach Bruce Cassidy said. "I love what he's brought so far. He's out there playing pucks, making it a little easier on the defense. He controls rebounds well."
Frederik Andersen made 20 saves for the Hurricanes (43-13-8), who had won four in a row and remained in first in the Metropolitan Division, two points ahead of the New Jersey Devils.
"You've got to give their team credit," Carolina coach Rod Brind'Amour said. "They played a real good, solid game. Their goalie was the difference. He's been a champ his whole career. He's got that in him. Unfortunately, it was against us."