The Sounders were trailing 2-1 in the 70th minute when Neagle drew a penalty after being tackled in the area by Vancouver's Greg Klazura, and Carrasco followed with a penalty shot goal -- his first career MLS tally.
Seattle (6-4-3) then netted the game-winner in the 81st minute after Obefemi Martins fired a low cross into the 6-yard box and Neagle put it in for his fourth goal of the season.
Andy Rose also scored for the Sounders, who won in front of 53,679 fans at CenturyLink Stadium.
Camilo Da Silva Sanvezzo scored twice within 16 minutes in the first half for the Whitecaps (4-5-4).
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