Elias Lindholm and Nazem Kadri scored in the third period to tie it 2-2 and help earn a point for the Flames, who couldn't score in the shootout and fell one point behind the Winnipeg Jets for the second wild card into the Stanley Cup Playoffs from the West with two games remaining.
"A sour taste from this one," Lindholm said. "It's going to sting a little bit."
Winnipeg, which has a game in hand on Calgary, defeated the Nashville Predators 2-0 earlier Saturday.
Jacob Markstrom made 31 saves for the Flames (37-27-16), who lost for the second time in the past seven games (5-1-1).
"Sloppy start, sloppy first period, then the second and third, I think we were the better team," Flames defenseman Rasmus Andersson said. "We had some long offensive] zone shifts and created some looks, but [goalie
[Thatcher] Demko
was kind of standing on his head. Second, third and overtime, we probably deserved to get that extra point, but it doesn't happen. It's frustrating, but we move on."
Demko made 41 saves, Cole McWard scored his first NHL goal and Andrei Kuzmenko scored the only shootout goal in the first round for the Canucks (36-36-7), who have won consecutive games after a four-game skid (0-2-2).
"We know where they are, so we know they were going to come out hard and we wanted to match that, and I think we did a really good job," Vancouver forward Elias Pettersson said. "I think we let our foot off the gas, but other than that I'm happy with our team."