Adam Ruzicka scored for the Flames, as did Tyler Toffoli who notched his 200th career tally.
Dan Vladar got the start between the pipes, his second of the trip and fifth of the season.
He made 30 saves in the game.
Antti Raanta got the start for the Hurricanes, returning after missing four games with injury. He made 19 stops.
Speaking of injuries, Michael Stone returned to the Flames lineup after being sidelined 10 games.
The Flames finished their season series against the Canes at 1-1 after beating them 3-2 in overtime back on Oct. 22 at the Scotiabank Saddledome. They trailed 2-0 in the first period in that one but battled back with Toffoli winning it late in extra time.
Chris Tanev made a lovely pass to try and spring Mikael Backlund in the opening minutes of the game, but he lost the handle and couldn't get a shot off.
Elias Lindholm showed off his speed and determination not long after, skating hard back nearly the length of the ice to break up a 2-on-1, getting his stick on the puck as it came across for a one-timer attempt by Brett Pesce.
At the other end, Toffoli undressed Jesper Fast, tucking the puck between the legs and walking around him, but fired one off the post.
Seth Jarvis would open the scoring at 6:20 with a cross-ice tip right by the post off a pass from Brent Burns that Vladar had no chance on.
The Calgary goalie made two incredible back-to-back saves on Paul Stastny from point-blank range in the slot just past the midway mark of the frame, part of a flurry of Canes chances where the Flames 'tender stood tall.