In the extra session, Bieksa fired a wrister on net from the high slot that Ebbett got a stick on in front of the net to get it past Antti Niemi.
"It was a pretty intense game out there tonight," said Luongo. "There wasn't much room out there and guys were mixing it up."
The first goal of the game went to Vancouver at the 11:12 mark of the first as Sedin used a wraparound from the left side.
Just under three minutes into the second, the Canucks took a 2-0 lead on the power play when Alexander Edler blasted a shot from the left circle and Kesler was on the doorstep to sweep the rebound in.
San Jose, though, made it a one-goal game at the 11:01 mark of the middle frame when Couture beat Luongo cleanly with a wrister on the fly from the left circle.
Just over five minutes later on the power play, it was a tie game as Thornton brought the puck out from the deep right boards and snapped it high into the net.
San Jose plays in Vancouver on Monday...The Canucks play at Anaheim on Friday...Vancouver took the previous meeting, a 3-2 win at San Jose on Nov. 26...Both teams went 1-for-4 on the power play.