Quick -- a finalist for the NHL's Vezina Trophy for best goaltender -- stopped all 16 shots he saw over the final two periods for the eighth-seeded Kings, who came up with a road victory to open the Western Conference series.
Los Angeles scored the go-ahead goal while shorthanded late in the second period when Dustin Brown broke in alone on the Blues' Brian Elliott, who made the stop but left a rebound for defenseman Matt Greene.
Slava Voynov also scored and Dustin Penner added an empty-netter for the Kings.
David Backes got the only goal for No. 2 seed St. Louis.
Elliott finished with 26 saves.