Chris Wondolowski scored first, his 11th of the season, but Hassli's first of 2012 sealed the game in Vancouver's favor.
The teams traded headers in the first half.
First, Chris Wondolowski found space at the back post to push Marvin Chavez's cross past former 'Quakes 'keeper Joe Cannon. Wondo leads MLS with 11 goals from 10 games.
Gershon Koffie equalized with a falling backwards header on a Camilo free kick.
San Jose, playing its third game in eight days, thought it had done enough to leave Canada with a point. But Hassli picked stoppage time to open his season scoring account. His goal delighted the B.C. Place fans and won the game for the Whitecaps.
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