The Canucks scored three straight goals in the third period to lead 4-3, but with Flames goaltender Joey MacDonald on the bench for a sixth attacker David Jones sent the game into extra time with 19 seconds remaining in regulation.
Dale Weise, Jannik Hansen and Santorelli scored in the third after the Canucks fell behind 3-1 early in the period. Canucks backup goaltender Eddie Lack made 32 saves in his first regular-season NHL game and David Booth scored for Vancouver in the first period.
Mikael Backlund, Sean Monahan and captain Mark Giordano also scored for the Flames and MacDonald stopped 23 shots. It was the second goal in three games for 18-year-old Monahan, who was selected sixth overall by Calgary in this year's draft.
Booth earned his 200th career point deflecting Jason Garrison's shot from the blue line low past MacDonald's stick at 4:47 of the first for a 1-0 Vancouver lead.
Giordano scored his first goal of the season and team-leading fourth point on a long wrist shot that beat Lack top shelf at 14:32 of the first to tie the game.
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Backlund scored on a breakaway on a T.J. Brodie stretch pass at 11:26 of the second. Backlund deked Lack and shoveled a backhand by the Vancouver goaltender's outstretched pad to put Calgary up 2-1. Monahan extended Calgary's lead at 1:47 of the third. Gaining an outside lane in the offensive zone, he took a pass and slipped the puck under Lack.
Hansen scored at 5:01 to cut into Calgary's lead and Canucks captain Henrik Sedin dished to Santorelli at the top of the offensive zone to tie the game 3-3. Daniel Sedin corralled a Curtis Glencross giveaway behind the goal-line and dished it out front to Hansen in the slot, while Santorelli fooled MacDonald with a wrist shot.
Brad Richardson fed Weise with a wraparound pass to put the Canucks ahead by a goal at 16:06.
NOTES: Singer Corb Lund sang "Blood, Sweat and Water" during the pregame ceremony in honor of Calgarians efforts after the June floods that destroyed the lower level of the Saddledome. ... Calgary fell to 18-15-7 in home-openers. ... Flames forwards Mike Cammalleri (wrist) and Matt Stajan (leg contusion) and defensemen Chris Breen (shoulder) were Calgary's scratches. ... Forward Alex Burrows was out of Vancouver's lineup.
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