Coyle’s four points tied an NHL-career high.
Mason Marchment and Mathieu Olivier also scored, and Adam Fantilli and Cole Sillinger each had two assists for the Blue Jackets (35-21-11), who are 6-0-4 during their point streak and 17-2-4 over their past 23 games. Jet Greaves made 27 saves.
Columbus pulled within one point of the Detroit Red Wings for the second wild card into the Stanley Cup Playoffs from the Eastern Conference.
Andrei Svechnikov scored, and Brandon Bussi made 24 saves for the Hurricanes (42-19-6), who had won four of six.
Marchment’s power-play goal gave Columbus a 1-0 lead at 5:25 of the first period with a one-timer low in the left circle off a pass from Coyle. It came during the first half of a double minor to Seth Jarvis for high-sticking Zach Werenski.
Coyle also scored on the power play at 19:05 to make it 2-0. He received a pass from Fantilli on the forehand near the left post, pulled the puck back and flicked it in.
Svechnikov cut it to 2-1 at 14:05 of the second period during 4-on-4 play, scoring on the rush with a backhand around Greaves.
Danton Heinen extended it to 3-1 at 17:29 with his 100th NHL goal after he poked the puck from Bussi behind the net. Bussi went down and Coyle’s shot into the open net was blocked by Alexander Nikishin, but the puck went to Heinen for a shot into the open net as Bussi scrambled back to the crease.
Denton Mateychuk scored 34 seconds later to push it to 4-1, finishing from the high slot after Sean Monahan’s face-off win.
Olivier made it 5-1 at 7:38 of the third period when he retrieved a loose puck in the slot from a Coyle one-handed assist after splitting two defenders.