Quick was busiest in the third period when he made 11 saves, completing his first shutout since returning Jan. 4 from a pulled groin that caused him to miss 24 games.
Los Angeles broke through for the game's only goal 24 seconds into the third period when Dustin Brown scored on a backhander at the end of a 3-on-1 rush.
The Kings rebounded from a 3-1 Saturday loss to Detroit in the chippy contest, which featured 109 total penalty minutes.
Eddie Lack turned aside 19-of-20 shots for the Canucks, losers of six in seven games.
Celebrity Families of 2014 [PHOTOS]