Quick turned aside all 19 shots he saw for the Kings, who logged their 40th win of season and increased their Pacific Division lead over idle Phoenix to two points with two games to play.
The Coyotes have three games left.
The Kings, who set a franchise record with their 11th shutout victory in a season, got third-period goals from Slava Voynov and Dwight King.
Devan Dubnyk stopped 35-of-37 shots for the Oilers.
Celebrity Couples of 2014 [PHOTOS]