The second period saw special teams come into play - and with them, even more Smith. The Flames killed off both of Mark Giordano's tripping penalties, but were unable to capitalize on their only powerplay of the game, with Nick Foligno sitting in the box for hooking.
Smith took over the rest of the way, an absolute force in keeping Columbus from converting on any of their chances.
He kept the game tied through regulation, including at a point with just over seven minutes left in the third period, in which Smith's desperation dives - along with some help from Michael Stone - took away what looked to be a sure goal for Columbus.
"It's the least I can do to help (Smith)," Stone said.
"He was outstanding again tonight. Got one point. I think he's a big reason for that.
"He's a competitive person. He hates to lose. Especially when he plays the way he played, you want to reward that."
Anderson scored the lone goal of the game just over two minutes into overtime, beating Smith just over his glove off of TJ Brodie's turnover.
"Those happen," Gulutzan said. "I mean (Brodie)'s handled the puck like a champ all night and then he's got control of it and it just pops off his stick. Those things happen within a game.
"It's a mentality, and it's a buy-in completely from all the guys, and you need to play in these tight-checking games to recognize its value, and that's what young teams go through.
"This one there's a lot of learning to do, and the guys recognize it."
ONE-TIMERS: Plenty of games played milestones coming up, as Smith played in his 493rd career game, Giordano in his 694th, Micheal Ferland in his 193rd, and Matthew Tkachuk in his 96th … Mikael Backlund sits at 99 career goals … Brodie has 195 career points … Gaudreau's goal-scoring streak was snapped at six games, and his points streak at 10.
NEXT UP: The Flames close out their six-game road trip with a back-to-back in Dallas (Friday, 7 p.m. MT) and Colorado (Saturday, 8 p.m. MT). They'll be back at the Scotiabank Saddledome on Tuesday to host the Toronto Maple Leafs (7 p.m. MT).