Quick, who registered 10 shutouts in the regular season, turned aside 16 Canucks shots in the final period to preserve the triumph for the Kings, who have forged surprising a 3-0 lead in their Western Conference quarterfinal series.
Dustin Brown broke up a scoreless tie 6:30 into the third period, hammering home the rebound of a Justin Williams shot for the game's only goal.
With the victory, the eighth-seeded Kings pushed Vancouver -- who won the President's Trophy for the NHL's best regular-season record -- to the brink of elimination.
Corey Schneider stopped 19-of-20 shots in the Canucks' loss.
The Kings will try to complete a series sweep in Wednesday's Game 4 at Staples Center.