Wright-Phillips unleashed a shot from about 30 yards that beat goalkeeper Jay Nolly.
It was his second goal in as many games on Man City's North American tour, having scored in a 2-0 win over Club America in San Francisco on Saturday night (Sunday morning UAE time).
Wright-Phillips almost had a second goal, but Nolly made a save late in the game.
Mario Balotelli's header in the 68th minute gave City a 1-1 tie after Brazilian striker Camilo opened the scoring for Vancouver, shocking the FA Cup champions before 24,074 fans with a header that deflected in off a defender.
Balotelli came to the far post to nod Andrea Mancini's high corner kick behind Nolly.
The match featuring a UEFA Champions League team that finished third in the Premier League last season and the worst team in MLS was played on a temporary grass field that had been deluged by rain on Saturday.
The field appeared relatively dry by Monday's kickoff, but the expansion Whitecaps were forced to cancel a league game against Real Salt Lake because of field conditions on Saturday.
Camilo gave Vancouver the lead in the 30th minute when he controlled Shea Salinas' cross and his shot deflected off defender Stefan Savic and past England goalkeeper Joe Hart.
Earlier in the half, Camilo narrowly missed on a free kick from about 28 yards and directly in front of Man City's goal. His strike cleared the City wall and fully extended Hart, who got a hand on the ball which deflected off the post.
Eric Hassli, in his first game after missing two with a foot injury, forced Hart to tip his shot over the bar.
City, with runs down the right flank by Dedryck Boyata and Bosnian international Edin Dzeko, also had some chances that were either missed or foiled by Nolly.
Savic was open when he missed an early header while Nolly made a good near-post save on Dzeko, who was open late in the half but fired a cross well wide.
City lost Ivory Coast star Yaya Toure in a first-half collision with Vancouver defender Michael Boxall. Toure left the game favoring his right leg.