The Czech center put the puck into the net at 2:53 of the third period after it deflected off the back of a Calgary defenseman's head. Kevin Bahl.
Chytil followed just under six minutes later, taking the puck from Arshdeep Bains and streaked across the ice before firing up and over the Flames goalie. Dustin Wolf.
Morgan Frost scored Calgary's lone goal, beating Demko 13:06 into the third period.
Wolf, playing his second game in as many nights, made 21 saves for the Flames, who cruised to a 4-3 shootout victory over the Oilers in Edmonton on Wednesday.
Canucks: The home team's offense picked up steam in the third period, with the Canucks putting 10 shots on net and scoring four goals in the period.
Flame: The team saw two players go to the locker room to be checked for visible head injuries. Connor Zary went down the tunnel after being pinned early in the second period but returned before the end of the frame. Bahl was eliminated after hitting a puck with the back of his head early in Game 3 and did not return to the ice.
Demko made a pair of key stops in the final seconds of the second period, first denying Matvey Gridin from long range and then sliding through the crease to stymie Yegor Sharangovich after he fired a low shot.
The Flames beat the Canucks 36-20.
Canucks: Visit the Edmonton Oilers on Saturday.
Flames: Host the St. Louis Blues on Saturday.