Sam Reinhart scored, and Anthony Stolarz made 22 saves for the Panthers (18-11-2), who lost three of the final four games of a season-long five-game road trip.
"I think we've left some out there," Reinhart said. "We see some success. We see when we have the puck we're playing well. It's an easy one to learn from. It's time to get back home, reenergize, and get ready for two big ones before Christmas."
Backlund gave the Flames a 2-1 lead at 3:31 of the third period, lifting a backhand over Stolarz's glove on a breakaway that was created by a turnover by Reinhart at Calgary's blue line.
"We've got some players that can skate well, and if there's a chance, we talked about that we don't cheat for chances, but if the play's there we go for it," Backlund said. "If we can find a way to score some big goals, that's big for the team."
Coleman was awarded the goal that made it 3-1 after he was tripped while attempting to shoot into an empty net on another breakaway at 18:24.
The goal came shortly after Markstrom made a right pad save on Sam Bennett at the edge of the crease while he was without his stick.
"He was great," Backlund said. "He played really well, really solid. Great to see him come in first game back and play that well. I'm really happy for him."
Martin Pospisil put the Flames ahead 1-0 at 8:45 of the first period when he beat Stolarz short side with a backhand on a partial breakaway.