The loss added to a tough stretch for the Sharks, who are 1-8-1 in their past 10 games and havent had a regulation win since March 12.
Vancouver trailed 2-1 midway through the third period, but quick goals from Pearson and Granlund swung the game.
Granlund broke the tie for the Canucks, completing the come-from-behind victory with a gritty goal 13:39 into the third.
With heavy traffic in front of the San Jose net, the Vancouver center banged away at the puck and found a way to shovel it in behind a diving Jones.
The Canucks scored on their first shot of the game after Horvat sliced a back pass to Pearson from below the goal line.
The left wing snapped the puck past Jones 1:28 into the game.
Labanc scored for San Jose, tipping a long shot from Brendan Dillon in past a diving Demko at 5:09 of the first.
The goal extended Labancs points streak to six games, including three goals and three assists.
The Sharks added a power-play goal 10:47 into the period after Vancouvers Adam Gaudette was called for hooking.
Tomas Hertl sent a pass down low and Pavelski tipped it in back door.
Pavelski returned to the San Jose lineup after missing seven games with a lower-body injury.
Joe Thornton had assists on both Labanc and Pavelskis goals.
The 39-year-old center has 1,063 assists, tying him with Steve Yzerman for eighth place on the NHLs all-time assists list.
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