The Sharks took a 2-0 lead in the best-of-seven series, which shifts to San Jose for games Sunday and Tuesday. San Jose was 17-2-5 at home this season.
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"I think it shows a lot about our team," said Torres. "We give up the lead, they were playing great. They were coming at us with everything. We showed a lot of determination, a lot of perseverance."
The Canucks took their sixth consecutive loss in a home playoff game. Now, they might not get another one after winning their fifth consecutive Northwest Division title.
Ryan Kesler scored two third-period goals for Vancouver, helping the Canucks overcome a 1-0 deficit that stood since the first period.
"I thought we played exceptional tonight," said Kesler. "We just didn't get it done. We have to regroup and focus on Game 3. Tomorrow we will learn from this and move on."
The Sharks outshot the Canucks 33-31 as Vancouver's Roberto Luongo and San Jose's Antti Niemi waged a goaltending battle for most of the game.
Shortly after getting hurt blocking Jason Garrison's shot, Thornton put in a rebound while falling down after Luongo stopped Brent Burns' deflection. The Sharks outshot the Canucks 10-4 in the first period after recovering from a slow start
San Jose had a goal disallowed at 6:08 of the second period. Joe Pavelski put in his own rebound but Tommy Wingels was deemed guilty of incidental contact with Luongo as he knocked him into a goalpost.
Luongo came up big near the midway mark as he stopped Torres, sprawling and catching the puck after a Vancouver giveaway.
Kesler created a 1-1 tie just 59 seconds into the third period as he put home a slap shot from the blue line during a power play. The goal came 20 seconds after San Jose's Andrew Desjardins was sent off for tripping Alex Edler.
Kesler put the Canucks ahead just over seven minutes later after a San Jose giveaway. Sharks defenseman Dan Boyle passed it up the middle and it deflected off Pavelski's stick and right to Kesler alone in the high slot. He ripped a slapper over Niemi's outstretched leg and blocker.
But Marleau forced overtime during a wild scramble. He poked in a puck that was lying in the crease after his shot squeezed through Luongo's legs and came to rest just in front of the goal line.
Just over a minute into overtime, Edler clanked a shot off the crossbar, and with Vancouver pressing, San Jose coach Todd McLellan called a timeout. Moments later, Torres scored on a 2-on-1 with Burns to give the Sharks the win.
- Vancouver converted 1 of 3 power-play chances while San Jose was blanked on five.
- Sharks winger Martin Havlat missed the game due to an undisclosed injury suffered in Game 1.
- Rookie Joe Cannata again served as Luongo's backup as Cory Schneider continued to recover from an undisclosed injury suffered late in the regular season. Schneider took the morning skate, but the Canucks had not yet decided whether he will travel to San Jose.