Monahan gave the Flames a 1-0 lead at 10:07 of the first period off a rebound after Crawford made an initial save against Lindholm.
Toews tied it 1-1 at 11:33 of the first when he shot it between Smith's pads on a breakaway.
Lindholm made it 2-1 at 7:18 of the second period, 10 seconds into Chris Kunitz's five-minute penalty for elbowing Hamonic. A video review determined Crawford gloved the puck behind the goal line.
Ryan made it 3-1 on the same power play at 8:44 off a pass from Noah Hanifin.
"It's nice to be able to capitalize and make them pay, get two on the major," Hamonic said. "That was the turning point. We were able to get those two and hold on."
Strome's power-play goal cut the Flames lead to 3-2 at 15:45 of the second.
"We've just got to find a way to break out of it," Strome said. "Thought we played a pretty good game tonight, actually. [We] didn't have the best first period, but we held in there and Corey was unreal for us in the beginning and throughout the whole game, obviously. But in the beginning, I think he made 15, 16 saves in the first period so that was obviously important for us to get out of there with a 1-1 tie.
"We were the better team for the last two periods, but they got the two points. [We've] got to find a way to break out of it and get the win here."