CALGARY, Alberta -- Although his team trailed 1-0 through two periods, Michael Frolik had confidence that the Calgary Flames could beat the Arizona Coyotes.

Frolik was right as he drew an assist on linemate Matthew Tkachuk's third-period goal before scoring 49 seconds into overtime to lead the Flames to a thrilling 2-1 win over the Coyotes.

"We just said in the room after the second that we're going to get one and we're going to win the game," said the right winger, who leads the Flames (7-10-1) with six goals and six assists through 18 games. "We did exactly that, and it's definitely a big two points."

Frolik stole the puck from Coyotes right winger Brad Richardson in the neutral zone before skating into the Arizona zone and snapping a perfect shot to the top corner past goalie Mike Smith.

"I had a few chances there and he made some great saves," Frolik said. "In the end, you just want to try to stick with it. I just tried to shoot it glove side, and I'm happy it went in."

Making his second consecutive start for the Flames, goalie Chad Johnson finished with 20 saves to improve his record to 4-2-1. Just one night earlier, Johnson stopped all 27 shots he faced to backstop the Flames to a 1-0 road win over the Minnesota Wild.

Right winger Tobias Rieder scored for the Coyotes (5-9-1), who have dropped three straight decisions.

"We just weren't good enough," Rieder said. "We made too many mistakes, gave them too many chances. The only reason we were in this game (is) because (Smith) played unbelievable today."

Smith made 22 saves in a losing cause. Despite sitting out Arizona's past 12 games with a knee injury, Smith looked sharp in his first game since Oct. 18.

"We lost. It wasn't good enough," said Smith, who was disappointed that Tkachuk's goal got behind him from a bad angle after it bounced off his helmet. "It was an unfortunate bounce there off the helmet and in. It could've been a 1-0 game and we're feeling a lot different coming into the locker room tonight. Any time a goal like that goes in is deflating for the whole team. That's on me, that one."

The Coyotes opened the scoring when Rieder deposited a rebound past Johnson with just 17.6 seconds remaining in the middle frame.

Left winger Jordan Martinook did a good job to keep the puck in at the point before firing a desperation shot on net that Johnson stopped, but Rieder snuck in behind the defensive pairing of Dennis Wideman and TJ Brodie to get himself into perfect position to get to the puck first.

Tkachuk pulled the Flames even at 6:40 of the third when his shot snuck into the top corner after the fortunate bounce off Smith's helmet.

"There wasn't much room, so I had to bank it off his head," Tkachuk said. "I just tried to get the puck to the net and hopefully something good would happen."

The Coyotes carried the majority of the play in the first period and held a 5-1 advantage in shots through the first 10 minutes.

Late in the first, Smith stopped a shot fired by defenseman Dougie Hamilton that was deflected by Coyotes left winger Lawson Crouse.

Before the middle frame was a minute old, Smith kicked out his left pad to turn aside a shot off the stick off Frolik and then made a shoulder save to deny a scoring attempt by Brodie.

Just past the five minute mark of the second, Smith made a great glove grab to stop a shot from the slot by Frolik.

NOTES: Flames LW Johnny Gaudreau had surgery on Wednesday to repair a fractured finger he sustained after scoring the winning goal in Calgary's 1-0 road win over the Minnesota Wild the night before. ... With Gaudreau out, C/LW Sam Bennett moved into his spot on Calgary's top line with C Sean Monahan and RW Troy Brouwer. ... After being scratched on Tuesday, RW/C Linden Vey started Wednesday's game on a line with C/LW Matt Stajan and RW Alex Chiasson. ... The Flames scratches were D Jyrki Jokipakka and C Hunter Shinkaruk. ... The Coyotes assigned G Justin Peters and C Christian Dvorak to the AHL's Tucson Roadrunners on Tuesday, making room for G Mike Smith and C Martin Hanzal to return to the lineup. ... Arizona scratched C Dylan Strome, D Connor Murphy and D Jakob Chychrun. ... While the Flames played their second game in as many nights, the Coyotes will do the same as they head to Vancouver to play the Canucks on Thursday.