Arvid Soderblom made 37 saves in his first NHL start for the Blackhawks (11-17-4), who were coming off a 6-1 loss at the Nashville Predators on Saturday and are 0-2-2 in their past four games.
"I think obviously yesterday was not a good game. Today I thought we played a little bit better, but still too many mistakes, leaving our goalie out to dry," Chicago forward Alex DeBrincat said. "That's what's going to happen when you play against a good team and give them chances like that."
DeBrincat put Chicago ahead 1-0 at 9:41 of the first period with a one-timer in the slot off a pass by Patrick Kane from behind the net. DeBrincat has scored four goals in his past five games.
"We can make excuses all day, but rust or no rust, we didn't play well," DeBrincat said.
Tkachuk tied it 1-1 when he redirected Gaudreau's centering pass by Soderblom's blocker at 13:13. He has scored six points (three goals, three assists) in a three-game point streak.
Elias Lindholm put Calgary in front 2-1 at 9:08 of the second period with a shot stick side from the top of the right circle on the power play.
Trevor Lewis extended the lead to 3-1 with a shorthanded goal at 17:46. His goal came 24 seconds after Soderblom made a glove save on Mikael Backlund's breakaway attempt.
"It was a good play by [Blake Coleman]," Lewis said. "He won the battle and got me the puck and I put it home. It was a big goal for sure. Obviously, special teams was huge for us tonight with the power play getting in there, too."
The Flames tied a franchise record with 26 shots in the second period. They also had 26 in the first period of a 6-6 tie against the New Jersey Devils on January 22, 1986.
"We talked about it in-between periods that we need to come out better and get our game in order and play the way we're used to," Lindholm said. "I think the second period showed how we can play when we play good hockey, and have a lot of shots and create a lot of chances. It was a fun period to be a part of. Want to see more of that."