Quick, who blanked St. Louis Tuesday, is the first goaltender in the NHL this season to record two shutouts. He has 16 for his career.
The Kings won their third in a row and handed the Coyotes their second consecutive loss.
Both goals came in the second period -- Dustin Brown scoring on the power play 56 seconds into the stanza and Kyle Clifford adding to the lead with 4:37 left.
Mike Smith stopped 20-of-22 shots for the Coyotes, who were shut out for the first time this season.