Carter's first goal came with 7:55 left in the third period and broke a 1-1 deadlock.
Carter padded the final margin with an empty-netter as the Kings snapped a five-game losing streak.
Dustin Brown also scored and Quick turned aside 27-of-28 shots.
Roberto Luongo made 46 saves for the Canucks, who dropped a second straight following a three-game winning streak.
Ryan Kesler got Vancouver's only goal.