Karri Ramo delivered just what they needed.
The Flames snapped their skid and handed the Hurricanes their second successive shutout defeat.
"It was probably our best team effort of the season," Calgary coach Bob Hartley said. "We had quite a good first period, and I felt we pressured them and gained the momentum. Carolina came hard at us, and we did a great job."
Carolina's offense has been shut down for two games following a season-best, five-game winning streak. The Hurricanes failed to match Calgary's intensity at the start, and were shut out for the fourth time this season.
"We spent too much time in our own end," defenseman Brett Bellemore said. "We didn't get off to a good start and they kind of got a lucky bounce off a skate or something [on their goal]."
The Hurricanes now have a long wait before they host Florida on Saturday.
"We didn't have that extra jump," Carolina coach Kirk Muller said. "It's disappointing. We have four days ahead of us to sit on it. When you play teams like Calgary, it's going to be a game in the trenches.
"They got the lead, and once they did, they were able to sit back a little bit and defend."
Backland scored his seventh goal of the season for the Flames, who notched their second power-play tally in 26 chances. Backland gathered the puck in front after it bounced off the skate of Hurricanes forward Radek Dvorak.
"It was nice to score first," Backlund said. "It's easier to play with some energy when you score than have to chase all the time like we've been doing lately."
Monahan scored his 13th goal midway through the third period to add some insurance. He scored into an open net after goalie Anton Khudobin was unable to get back across the crease from the far post.
Ramo improved to 8-8-3 as the Flames swept the two-game season games from Carolina. It was Calgary's first shutout in 117 games.
"It's good that it's out of the way," Ramo said. "It's nice to finish one without a goal. Obviously, everyone thinks about it and knows the situation but you just have to focus and play normally."
Khudobin, who lost his second straight, did some of his best work in the first period when the Flames carried the play and held a 14-5 shots advantage. Khudobin made 27 saves overall.
Carolina captain Eric Staal returned to the lineup after missing three games because of a lower-body injury.
Calgary is 11-3-3 in games in which it scores a power-play goal. The Flames went 1 for 3. ... Carolina activated C Jiri Tlusty from the injured list, and he was in the lineup for the time since Dec. 23, before he was sidelined because of an appendectomy. ... The Flames have won three straight and four of five against Carolina. ... Calgary RW Kevin Westgarth returned to face his old team for the first time since being traded by Carolina on Dec. 30.