Colton cut it to 5-4 at 11:20 of the third after Josh Manson’s point shot caromed off the skates of Sharangovich and Zary and landed on his stick.
Rantanen ended a nine-game goal drought when he tied it 5-5 at 13:31, deflecting Makar’s shot from the right circle.
Kadri gave Calgary a 1-0 lead at 13:46 of the first period with a wrist shot from beyond the left circle after a giveaway by Rantanen in the neutral zone.
Tomas Tatar tied it 1-1 at 18:14 with his first goal of the season after he sent Colton’s pass from behind the net over Vladar’s blocker.
Makar gave Colorado a 2-1 lead on a power play at 1:43 of the second period, one-timing a centering pass from Rantanen to the far side.
MacKinnon extended his point streak with an assist on Makar's goal.
"I'm doing everything I can to be ready to go off the ice,” MacKinnon said. “Obviously no one sees that stuff, but that's kind of what is making me play well on the ice right now. It's a lot of time and effort, so I'm glad it's paying off.
“Obviously, my job is to lead by example more than anything, and I think Cale and Mikko are all doing the same thing as well.”
Andrew Mangiapane tied it 2-2 at 5:14 with a one-timer from between the circles that beat Gerogiev’s blocker.
Coleman beat Georgiev with a snap shot from above the left circle at 13:21 to give the Flames a 3-2 lead.
“It just wasn't good enough,” Coleman said. “[We] knew they'd push. They're a good team. It's another lead going into a third. There's no business losing that game.”