Erik Hurtado opened the scoring inside two minutes before Nicolás Mezquida fired into the bottom corner to double the visitors’ lead.
Vancouver found themselves down to 10-men on 23 minutes when ‘keeper David Ousted brought down Chris Wondolowski.
The hosts pulled a goal back with a brilliant finish from Wondolowski before half-time and Nick Lima netted his first MLS goal just after the restart to level the game.
The comeback was complete 11 minutes from time when Anibal Godoy lashed home to deny the Whitecaps anything from the game.
Whitecaps race into early two-goal lead
San Jose managed to overcome Montreal Impact in the opening week of the new season, but found themselves behind early against Vancouver.
Defender Florian Jungwirth failed to clear a ball over the back line and Hurtado got ahead of two markers to strike the ball into the net off the inside of the post.
San Jose were stunned and found themselves two-behind before long as the visitors made the most of some fine work from Hurtado.
The forward drove into the area well and found Mezquida, who struck low across goal to double Vancouver’s advantage in the game.
However, the visitors found themselves down to 10-men just six minutes later when Wondolowski, who was through on goal, was brought down by the approaching Ousted.
Lima strikes after Wondolowski to level game
San Jose made the most of their man advantage and reduced the arrears on 32 minutes when defender Víctor Bernárdez’s pull-back was smashed home by Wondolowski.
It wasn’t long after half-time that the Quakes managed to level the game, with the hosts making the most of a swift break forward.
Godoy crossed for Wondolowski at the back post, and the forward then teed up Lima, who rifled past stand-in ‘keeper Paolo Tornaghi.
And they could have found themselves behind for the first time in the game, but Tornaghi managed to deny Simon Dawkins at his near post.
Comeback comepleted when Godoy lashes home
San Jose completed their remarkable comeback on 79 minutes when a magnificent strike from Godoy followed a great break forward, which had the visitors on the back foot.
The Panama international struck from 25-yards up and over the ‘keeper and into the roof of the net to spark jubilant celebrations from players and fans alike.