Brett Ritchie tied it 2-2 at 2:31 of the second period when he banked in a shot off Raanta's pad from the goal line.
Derek Stepan appeared to put Carolina back in front with nine seconds remaining in the second, but Flames coach Darryl Sutter challenged the play for offside, and the call was reversed after a video review.
"Third period we came back, did well ... got a goal that got taken back off the board, which [was the] right call," Hurricanes coach Rod Brind'Amour said. "[Markstrom] made a great save on another one. We all had our hands in the air thinking it went in. It wasn't our best, but I thought we worked really hard."
Markstrom made a sprawling save on a backdoor pass from Aho to Slavin at 6:31 of the third period, one of 12 saves he made in the period. Calgary then killed off Blake Coleman's double-minor for high-sticking Brent Burns at 13:24.
"The penalty killers were unbelievable," Markstrom said. "For everyone that was out there, I don't know how many different pairings on forward and [defensemen] that was out there for that four-minute kill. That was huge for us and after that, we grabbed the momentum."
NOTES:Aho has eight points (three goals, five assists) during a four-game point streak. ... Sutter coached in his 1,402nd NHL game, passing Ron Wilson for ninth in NHL history. … Hanifin had one shot, two hits, two blocks and a minus-1 rating in 23:26 of ice time after missing one game with an undisclosed injury.