San Jose is five points ahead of the fourth-place Calgary Flames, who can't catch the Sharks. Each team has two games remaining. Edmonton lost 6-4 to the Los Angeles Kings, and Calgary lost 3-1 to Anaheim.
WATCH: All Canucks vs. Sharks highlights
"We want to try to win out and give ourselves the best possible scenario going into the playoffs with home ice," said San Jose forward Chris Tierney, who scored a third-period goal. "We're just going to keep working every day, try to get better, and try to string a couple wins together here."
Martin Jones made 33 saves for the Sharks, who swept the season series against the Canucks (5-0-0), including a 3-1 win in Vancouver on Sunday in the first of the home-and-home set.
Sharks center Joe Thornton missed the game with a left-knee injury, ending his streak of 201 consecutive games. Center Logan Couture missed his fifth game since being hit in the mouth by a deflected puck against the Nashville Predators on March 25.
Even without their top two centers, the Sharks took control early.
Rookie Kevin Labanc and Joel Ward each scored in the first 30 seconds to give San Jose a 2-0 lead. They were the fastest two goals to begin a game in Sharks history. The old record was 47 seconds, set by Owen Nolan and Joe Murphy in a 2-2 tie with the Chicago Blackhawks on Oct. 22, 1998.
Labanc scored at 18 seconds of the first period, beating goalie Richard Bachman with a wrist shot from the right faceoff circle to end a 28-game goal drought.
Ward put a snap shot past Bachman 12 seconds later for a 2-0 lead.