Quick stopped all 27 shots he faced in backstopping the surging Kings to their 10th win in 11 home contests.
Rookie Tyler Toffoli notched his first career NHL goal and assist while Anze Kopitar also scored and added a helper for Los Angeles, which pulled into fourth place in the Western Conference standings with the win.
Mike Smith started in net for the Coyotes but was pulled in the third period after surrendering four goals on 22 shots.
Jason LaBarbara relieved and stopped 7-of-7 tries the rest of the way as Phoenix was shut out for the third straight game.
Celebrity Families of 2014 [PHOTOS]