The Flames dominated the opening minutes, firing three shots on Canucks goalie Alex Auld before Vancouver could test Flames stopper Miikka Kiprusoff.
Flames captain Jarome Iginla got off a wrist shot from the high slot with the team's best chance early but was turned aside.
Flames centre Ville Nieminen took the game's first penalty, boarding defenceman Bryan Allen at 7:09. The Canucks poured on the pressure but failed to score, with Kiprusoff using his blocker to stop a Daniel Sedin deflection from close range.
The Flames earned their first powerplay opportunity at 11:01 after Jarkko Ruutu body slammed Martin Gelinas but Calgary failed to generate a shot on goal with the man advantage.
Nieminen failed to bury another great chance at 13:40 when Auld couldn't corral a rebound.
With less than three minutes remaining, Iginla had his third great scoring chance, stealing the puck in the slot and sliding it wide of the Canucks cage.
Canucks outshot the Flames 7-6.
* FIRST-PERIOD FIRST STAR -- Jarome Iginla, Calgary
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The Canucks carried the play to the Flames early in the second period but goaltender Miikka Kiprusoff continued to look sharp.
Flames winger Martin Gelinas forced Alex Auld to make a quick glove save four minutes into the period, racing down the left wing before rifling a shot from the top of the circle.
Canucks left-winger Daniel Sedin failed to deflect a puck past Kiprusoff seconds later, Vancouver's best chance in the second.
With 13 minutes remaining, Flames winger Shean Donovan almost broke in alone on Auld but big Canucks defenceman Ed Jovanovski tied up the speedy winger as he broke into the Vancouver zone.
Vancouver defenceman Brent Sopel had a knee-on-knee collision with Flames winger Oleg Saprykin at the midway mark, sending the Calgary forward to the bench favouring his left knee but he never missed a shift.
Flames centre Craig Conroy was called for boarding at 10:39 providing Jovanovski and Marcus Naslund with great scoring chances from in close.
Seconds after Conroy's penalty expired, he picked up a pass at centre ice and fed Jarome Iginla streaking into the slot, who fired the puck through Auld's legs for a 1-0 lead at 12:50
Flames defenceman Steve Montador, getting his first start of the playoffs, mishandled a pass at his own blueline with three minutes remaining, allowing Jarrko Ruutu to steal the puck for a scoring chance.
Montator slashed Ruutu and served a two-minute minor.
Canucks outshot the Flames 10-6.
* SECOND PERIOD FIRST STAR -- Jarome Iginla, Calgary
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The Canucks benefitted from starting the third with 90 seconds remaining in a powerplay but failed to earn a shot on goal.
The Canucks continued pouring on the pressure with their defencemen pinching in to create scoring chances while Flames goaltender Miikka Kiprusoff needed to be sharp.
Sami Salo had half the net for a target six minutes into the period but couldn't find the handle.
Canucks forward Matt Cooke tied the game 7:32 into the period, whipping the puck past Kiprusoff from close range after Vancouver won the faceoff in Calgary territory.
Cooke then took a double minor mid-way through the period for high-sticking Flames defenceman Rhett Warrener in the face, drawing blood.
Seconds later, Flames right winger Jarome Iginla buried a powerplay goal, his second of the game, from the top of the Canucks crease while being crosschecked from behind as the Flames built a 2-1 lead.
With five minutes left, Flames centre Craig Conroy misfired from close range on what would have been the insurance goal.
Flames defenceman Andrew Ference broke his stick slashing Daniel Sedin with 90 seconds remaining.
Canucks forward Brendan Morrison had the best powerplay chance, firing the puck into Kiprusoff's chest from close range.
In the dying seconds of the period, Iginla missed the empty net by inches. On the ensuing rush, with just six seconds remaining, Marcus Naslund went to the net with backhand shot before Cooke buried the rebound to send the game into overtime.
* THIRD-PERIOD STAR: Matt Cooke, Vancouver.
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Starting with a powerplay, Flames captain Jarome Iginla fired a wrist shot at Canucks goalie Alex Auld and veteran winger Martin Gelinas buried the rebound just 1:25 into overtime.
* OVERTIME STAR: Martin Gelinas, Calgary
Frame by frame
DAN TOTH -- Calgary Sun
, Last Updated: 4:04 PM ET