Miikka Kiprusoff made 39 saves, and the Flames opened their season with a 5-3 win over the Canucks on Thursday night.
Rene Bourque, Brandon Prust and defensemen Mark Giordano and Adam Pardy scored for the Flames, and defenseman Dion Phaneuf added an empty-netter to seal the win. Calgary had lost six straight season-openers.
"Every time we play them, it's going to be a battle," Bourque said. "There's definitely guys that you don't like on that team and I'm sure they don't like us, either.
"Every game is going to be a war. I expect the next five of the regular season to be the same."
It was the first regular-season game for the Flames under new coach Brent Sutter and with defenseman Jay Bouwmeester in the lineup. Bouwmeester, signed to a $33-million, five-year contract, logged over 29 minutes in his debut.
"At the end of the day, teams are close in this league and a win's a win," the 25-year-old Bouwmeester said. "It's all good."
After Calgary's fourth goal, the Canucks held a 28-8 edge in shots the rest of the way.
"I'm not sitting here and doing handstands and thinking we played a great game, but we played a pretty darned good game for 38 minutes," Sutter said. "We backed off, and that's where we have to continue to work and push.
"Our goalie played very well. It's two points and it's a good win. There's work to be done."
Burrows pulled Vancouver to within a goal less than a minute into the third period. The Canucks scored twice on power plays in the second period and trailed 4-2 after 40 minutes.
"You can't spot a team like that a two- or three-goal lead and expect to win," Vancouver coach Alain Vigneault said.
Calgary had two man-advantage goals within 8 minutes of the first. An even-strength goal put the Flames in control.
Kiprusoff robbed Henrik Sedin twice in the third period. Just after a spinning stop against Sedin to open the period, Burrows tucked a rebound under Kiprusoff 41 seconds in.
The fourth line of Prust, Fred Sjostrom and Eric Nystrom combined on Calgary's fourth goal at 9:34. Prust dragged the puck out of the corner and scored his second NHL goal on a wraparound.
Bieksa's drive from the point deflected off the skate of Sjostrom for a power-play goal at 4:02.
Phaneuf's open-ice toppling of Vancouver's Daniel Sedin in the final minute of the first period, prompted a melee between all players on the ice at the buzzer.
Pardy padded Calgary's lead 11:52 of the first.
The Flames celebrated the start of their 30th year in Calgary by wearing retro jerseys from their inaugural 1980-81 campaign. The franchise was based in Atlanta eight seasons before moving to Alberta.
The Flames and Canucks will meet five more times and conclude the regular season against each other. ... Bouwmeester extended the NHL's longest current consecutive games streak to 343. ... Calgary enforcer Brian McGrattan (shoulder) is expected to play his first game Oct. 8 against Edmonton. ... Pavol Demitra (shoulder), D Mathieu Schneider (shoulder), forward Jannik Hansen (broken fingers), sat out for Vancouver. ... Calgary C Olli Jokinen played his 800th NHL game. ... Vancouver dropped to 21-15-3 in season-openers. The Flames are 12-15-10.