Jack Drury and Martin Necas each had two assists for the Hurricanes (31-17-5), who have won six of their past eight games.
Carolina took a 2-0 lead in the opening 4:50 of the first period.
“We started really well, which was great to see, and our goalie played really well, too, I mean ‘Kooch’ made some real good saves,” Hurricanes coach Rod Brind’Amour said. “We got ahead early and we kind of sat back, that happens, but the start was really good and made the difference.”
Dylan Guenther scored for the Coyotes (23-25-4), who are 0-7-1 since defeating the Pittsburgh Penguins 5-2 on Jan. 22. Karel Vejmelka allowed five goals on 26 shots before he was replaced in the third period by Matt Villalta, who made four saves in his NHL debut.
“The way we started was unfortunate, not because we didn’t play well, but [because] we need to be more detailed,” Arizona coach Andre Tourigny said. “And that’s on me. It’s my responsibility to make sure that doesn’t happen.”
Jordan Martinook scored 16 seconds into the first period to give the Hurricanes a 1-0 lead. Brady Skjei threw the puck on net from along the left-side boards, and Martinook switched to his backhand to put in the rebound.
“I thought we started on time, that goal was huge for us and got us going,” Carolina forward Michael Bunting said. “We didn't take the foot off the gas, and we played to our standard.”