After Andrew Desjardins gave the Sharks a 1-0 lead with a goal 7:41 into the first period, Thornton struck only 41 seconds later to double the advantage.
The San Jose center then assisted on Logan Couture's goal for a 3-0 advantage before the initial period was halfway over.
Antti Niemi turned aside 23-of-25 shots for the Sharks, who racked up their fifth straight win and strengthened their grip on the sixth seed in the Western Conference.
Cory Schneider made 32 saves for the fourth-seeded Canucks.
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