Slavin had a goal and an assist, and Pyotr Kochetkov made 15 saves for the Hurricanes (35-22-4), who have won two of three.
Nazem Kadri scored for the Flames (28-23-9), who were coming off 3-0 losses to the Tampa Bay Lightning and Florida Panthers on Thursday and Saturday. Dustin Wolf made 31 saves.
“For me, it’s finding a way to stick with it, and I thought the guys did tonight,” Calgary coach Ryan Huska said. “You go through these stretches during the season when you get into ruts; we’re in one offensively right now. But it will turn as long as the work and the compete is still there, and I saw that right until the end today.”
Slavin gave the Hurricanes a 1-0 lead with 35 seconds remaining in the second period. After skating the puck from the Carolina defensive zone and passing to Jackson Blake at the Calgary blue line, Slavin got behind Flames defenseman Kevin Bahl to redirect the return pass near the left post.
“I just got my feet moving up the ice, and I saw (Blake) streaking up the far side,” Slavin said. “So I figured I would get it in the skill guy’s hands. He obviously made a great play back to me.”
Kadri tied it 1-1 on the power play at 7:06 of the third period on a one-timer from the right circle off a pass from Jonathan Huberdeau.
“We were joking in the dressing room before the third that the ninth period is the charm for us,” Andersson said. “We managed to get one. Huge for our power play to step up there, and the PK was good all night.”