Matthew Tkachuk and Micheal Ferland scored in regulation for the Flames in the final 20 minutes. Tkachuk notched the shootout winner, while Sean Monahan also scored in the elimination frame.
"Well, after a couple of tough games at home, this is exactly what you need right now," Tkachuk said. "I mean, this is good vibes. This is everybody feeling confident, a great team win, great goaltending, and a comeback."
Mike Smith collected the 200th win of his NHL career, stopping 28 of 30 shots. He also stopped two of three in the shootout.
"Yeah, it's a growth game for sure," coach Glen Gulutzan said. "Because you're playing against a really good hockey club. I thought the atmosphere in the building was more intense than most of the regular-season games I think we've played so far. It had some real good energy. And to come back from behind against a really good hockey club, it's a growth game for our group."
Pekka Rinne, meanwhile, stopped 30 of 32 shots, thwarting the visitors for much of the night, until they were able to break through in the third period.
Filip Forsberg and Roman Josi both scored first-period powerplay goals to give the Predators the early lead, and Forsberg also had a shootout goal.
Recent call-up Mark Jankowski, playing in just his second NHL game, went to the box for a tripping call on Scott Hartnell in the Flames' end.
While the Flames had killed 19 straight penalties on the road coming into this game, Forsberg snapped that streak with a rebound goal over Smith to get the Predators on the board.
"Obviously the penalties and that, not the way I wanted it to go in my second shift, but I think the guys really rallied around it," Jankowski said.
Josi gave them a two-goal lead while Matt Stajan was sitting in the box for interference, firing a rocket from the top of the faceoff circle, high far-side and in.
The Flames had four powerplay chances of their own, and despite some close looks throughout, were unable to capitalize.
No matter, though, as Tkachuk got the Flames on the board eventually, outmuscling the Predators in their own zone to end Rinne's shutout bid and make it a one-goal game.