Marc-Edouard Vlasic and Evander Kane scored in the third period, and Aaron Dell made 23 saves for the Sharks (4-10-1), who have lost five straight, including 3-2 to the Winnipeg Jets on Friday. San Jose has been outscored 22-8 during the losing streak.
"Same problems that have plagued us a lot of the year, we get behind early," coach Peter DeBoer said. "Usually one of the first two or three chances ends up in the net, and we're playing from behind all night."
Vancouver, which was coming off a 2-1 overtime loss to the Anaheim Ducks on Friday, has outscored its opponents 49-27 while going 9-1-2 in its past 12 games.
"Guys are confident, and we're scoring some big goals," Demko said. "That's great, it helps me build some confidence as the game goes on, especially with the goals coming early."
Sutter put the Canucks ahead 1-0 on a rebound at 4:17 of the first period, sliding a backhand past a sprawling Dell.
Virtanen scored on a breakaway 45 seconds into the second period to make it 3-0. Dell appeared to make the save using his right heel to kick the puck out of the air, but video review showed the puck crossed the goal line.