Andrew Mangiapane gave the Flames a 1-0 lead on a snap shot from the slot at 12:11 of the first period.
Gurianov scored 38 seconds later with a wrist shot on the rush to tie it 1-1 at 12:49.
"It's tough," Gurianov said. "I mean, we've lost two games. We had goals and other penalties. It's kind of tough trying to get goals on the penalty kill and tough to get the game back."
Tkachuk's power-play goal from the top of the right face-off circle at 12:28 of the second period gave the Flames a 2-1 lead.
Monahan scored a power-play goal from his knees in the slot at 14:21 to make it 3-1.
"I thought we had a pretty good start," Monahan said. "There was energy throughout the lineup and when you move your feet and make stuff happen, you're going to draw penalties. Our power play was good tonight, and that's what won us the game."
Mikael Backlund scored Calgary's third power-play goal in front of the crease at 10:21 of the third period to make it 4-1. The Stars challenged for goalie interference, but the call on the ice stood and Dallas was assessed a minor penalty.
"It's huge," Lindholm said of the power play. "It all starts with the face-off; we switched it up a little bit and we're winning more pucks now. Hopefully, that creates more chances for us. Three goals today on the power play, so it was a good game."
Derek Ryan scored a shorthanded, empty net goal with 2:04 remaining for the 5-1 final.
"The NHL is all about the little things," Stars defenseman Roman Polak said. "We just need to focus more on the little things and play together more."