Yegor Sharangovich also had a goal and an assist, and Devin Cooley made 22 saves for the Flames (20-23-4), who had lost five of six.
Nick Foligno scored, and Spencer Knight made 20 saves for the Blackhawks (19-21-7), who have lost three of four.
Foligno opened the scoring for the Blackhawks at 2:38 of the first period, scoring on the second shot on goal of the game. Colton Dach fed the puck to Foligno from the left boards, and Foligno put a wrist shot from the slot past Cooley’s glove.
The Flames tied it 1-1 just 36 second later at 3:14 while on a power play. Sharangovich put in the rebound of a Connor Zary backhand shot from in close after Backlund got a touch on the puck during a net-front scrum for it.
Backlund scored short-handed at 6:05 to give the Flames a 2-1 lead. He stole the puck from Chicago forward Andre Burakovsky near the Flames’ blue line, skated in on a breakaway and scored on the forehand.
Matt Coronato scored with a wrist shot into an empty net at 18:59 of the third period for the 3-1 final.
