"I had three or four shots in a row but they kept being blocked or I missed the net," Bieksa said. "But the puck kept coming back to me and I found a way to squeak one in there."
After a scoreless overtime, Demitra was the only player to score in the shootout, snapping a shot from close in past Kiprusoff.
After misses by Michael Cammalleri and Jarome Iginla, Todd Bertuzzi almost tied the shootout on a nifty spin-a-round backhander with Luongo out of position, but the shot went off the goal post.
Calgary had taken a 3-2 lead at 6:52 of the third on Rene Bourque's 20th goal of the season.
The go-ahead goal was immediately preceded by a clutch pair of saves by Kiprusoff, who sprawled to make consecutive stops off Alex Burrows from close range, two of his 40 saves.
Kiprusoff's best save on a Canucks power-play with less than 10 minutes remaining and Vancouver pressing for the tying goal. Seemingly out of position on Kyle Wellwood's shot, Kiprusoff dove across and knocked the puck out of the air with the paddle of his stick, denying what looked like a sure goal.
"I thought I had an empty net but somehow he was able to reach back and stop it right on the goal line," Wellwood said. "That's definitely the best save I've ever had to deal with," said Wellwood."
Matching Kiprusoff save-for-save was Luongo, who finished the night with 38 stops as the two teams combined for 84 shots.
"I picked them up in the first 40 minutes and then they picked me up at the end," said Luongo, who finished with 38 saves. "We didn't play our best hockey the first two periods and then with us still tied I give up that goal. But that's what we do as a team, we try to bail each other out and tonight, you saw both sides of that."
Iginla and Daymond Langkow also scored for first-place Calgary, which leads second-place Vancouver in the Northwest Division by eight points. The Flames have picked up points in five straight games (3-0-2).
Iginla also added an assist giving him 823 career points (395 goals, 428 assists) and moving him past Al MacInnis (822) into second place on the Flames career scoring list. Theoren Fleury is on top with 830.
Vancouver improved to 6-1-0 in its last seven.
Notes: Wellwood's high-sticking penalty in the first period ended a string of 159 games without a penalty for the Vancouver forward. It had been three seasons since Wellwood was last in the penalty box, a minor penalty he took on Apr. 11, 2006 versus Florida ... Calgary rookie RW Brandon Prust (broken jaw) has been declared healthy after missing 30 games but he did not get back in the lineup ... Vancouver improves to 9-4-3 versus the Northwest Division.
|Jarome Iginla (21) ASST: Craig Conroy (24), Rene Bourque (19)|
1 - 0 CGY
|SHG - Ryan Kesler (17) ASST: Alexandre Burrows (15)|
1 - 1 Tie
|PPG - Ryan Kesler (18) ASST: Steve Bernier (15), Alexander Edler (22)|
2 - 1 VAN
|Daymond Langkow (18) ASST: David Moss (12), Curtis Glencross (18)|
2 - 2 Tie
|Rene Bourque (20) ASST: Jarome Iginla (40), Craig Conroy (25)|
3 - 2 CGY
|Kevin Bieksa (9) ASST: Willie Mitchell (15), Daniel Sedin (32)|
3 - 3 Tie
|1||M. Cammalleri||P. Demitra|
|2||J. Iginla||R. Kesler|
|Adrian Aucoin Roughing against Alexandre Burrows|
|Alexandre Burrows Roughing against Adrian Aucoin|
|Mattias Ohlund Holding against Jarome Iginla|
|Todd Bertuzzi Interference against Willie Mitchell|
|Jarome Iginla Hi-sticking against Alexander Edler|
|Kyle Wellwood Hi-sticking against Dion Phaneuf|
|Andre Roy Roughing against Darcy Hordichuk|
|Darcy Hordichuk Roughing against Andre Roy|
|Alexandre Burrows Roughing against Todd Bertuzzi|
|Todd Bertuzzi Roughing against Alexandre Burrows|
|Shane O'Brien Roughing against Todd Bertuzzi|
|Matthew Lombardi Tripping against Alexander Edler|
|Henrik Sedin Hooking against Craig Conroy|
|Kevin Bieksa Delaying Game-Puck over glass|
|Adrian Aucoin Delaying Game-Puck over glass|