There were plenty of great chances early but no goals, with the Coyotes edging the Flames 16-14 in shots over the opening 20 minutes.
"The first period was a little busy but not a whole lot of tough chances," said Smith. "It was a solid effort from our group. We blocked a ton of shots and did a lot of good things in front of me."
In the second, Jankowski opened the scoring with a goal everyone will be seeing on the highlight reel this week.
After taking a pass from Jaromir Jagr and being denied on his first attempt by Wedgewood, he grabbed the rebound and shot between his legs as he was almost behind the goal-line.
"I saw the puck pop out there and my only real shot was to try and go through the legs," said Jankowski. "Just a reactionary thing, not something I planned, and thank God it went in."
Smith made a handful of great saves in the second period, the best when he dove across and out of his net to stop a cross-crease one-timer by Alex Goligoski with his glove.
Just over five minutes into the third period, the Flames had a glorious chance to go up by a pair when team scoring leader Johnny Gaudreau redirected a lazer of a cross-ice backhand pass from Micheal Ferland but Wedgewood was able to get in front of it.
Later in the frame, Gaudreau was stopped twice more by Wedgewood - once after driving to the net around two defenders, the second on a partial breakway soon after.
The Flames finally got another puck past Wedgewood at 10:19 of the third, when Backlund scored his seventh goal of the season.
After some hard work behind the net by linemates Michael Frolik and Matthew Tkachuk, it was the latter who threw a backhand pass out to Backlund who one-timed it far-side.
Less than two minutes later, Jankowski potted his second of the game right off the face-off with another lovely ditty, grabbing the puck after Sam Bennett took the draw and going backhand, forehand around Wedgewood.
The two clubs will meet three more times this season.
