Lee Stempniak had opened the scoring for the Flames late in the first period before the Canucks (7-2-2) bagged two goals in a 27-second span midway through the second to seize control of the game.
Alexandre Burrows scored his third of the campaign before Jordan Schroeder claimed his first ever NHL goal to put the Canucks ahead, then Kevin Bieksa blasted a rocket from near the blue line late in the period to extend the lead to 3-1.
Chris Higgins added an insurance goal and Schroeder doubled his tally in the third period to ensure the Flames left Vancouver with a 3-4-2 record.
"You're gripping your stick pretty tight. It's excitement, relief, it's been eight games and it's kind of a weight lifted off the shoulders because you want that first one so bad," Schroeder, 22, told reporters of his breakthrough goal.
"To be able to get two in one night is always good."
Winger Burrows claimed Calgary's goal acted as a catalyst to wake the home side from their slumber and record a win that keeps them top of the Northwest Division and moved them up into third in the Western Conference.
"Our start wasn't the best but once they scored, we started passing a bit more and starting getting pucks deep and it's how we created a lot of offense tonight," Burrows said
"And we had four lines rolling and everyone was trying to join the party."