David Rittich also had a massive night, earning first-star accolades for his 34-save performance, including many clutch stops in the third and overtime.
Big Save Dave continues to be a wall for the Flames. His teammates, to a man, were quick to credit his play in the win.
The opening frame was back-and-forth, with Arizona getting the majority of early shots but the Flames eventually catching up, the visitors leading 10-9 in that category after 20 minutes.
Johnny Gaudreau had a golden chance to get his side on the board first, taking a pass in the high slot all alone and stepping into a slapshot but Raanta slammed his pads shut on the five-hole attempt.
Clayton Keller broke the goose egg at the 8:29 mark. Andrew Mangiapane lost the puck near the Calgary blueline and Nick Schmaltz ended up firing a cross-ice pass to Keller, who wired a one-timer from the right face-off circle as he faded backwards, beating Rittich short-side.
The Coyotes found themselves with a 2-on-0 while killing a powerplay later in the period and looking to double up their lead, but Michael Grabner's attempt was turned aside by Rittich.
The Flames started the second on the powerplay but no doing when it came to solving Raanta.
Mark Jankowski - one of two Flames forwards yet to bulge the twine this season - was sprung on a breakway while short-handed a few minutes later but fired the puck up and over the net trying to go short-side.
Christian Dvorak made it 2-0 with a fantastic tip right on the doorstep 4:09 into the period, redirecting a long pass from Phil Kessel who was up near the blueline.
With less than four minutes to go in the period, Tkachuk was hooked and pulled down as he tried to walk out from behind the net and wrap a puck around Raanta.
On the ensuing powerplay, Sean Monahan gained the zone and a few steps inside the blueline, slung a pass cross-ice to Tkachuk who one-timed it back across to Gaudreau on the doorstep to the left of Raanta for an easy redirect at 17:09.
It was Gaudreau's fourth goal of the season and first since Oct. 12.