Trailing 2-1 entering the final period, the Canucks scored twice within in a 1:19 span to stun the Sharks and grab the early advantage in the series.
Bieksa took a pass from Alexandre Burrows at the right point and unleashed a shot that found the left corner 7 minutes into the final frame, pulling the Canucks even.
Vancouver then took the lead after Dany Heatley was whistled for an elbowing penalty. On the ensuing power play, Christian Ehrhoff sent a pass from the left point onto the stick of Sedin, who switched to his forehand and pumped it past Antti Niemi.
Maxim Lapierre also scored and Roberto Luongo stopped 27-of-29 shots for the Canucks.
Joe Thornton scored an unassisted goal and Patrick Marleau added a goal for the Sharks, who will try to even the series in Game 2 Wednesday in Vancouver.
Niemi finished with 35 saves.