Quick has won three of his past four starts.
"He feels real good in the net right now, and we feel good with him in the net," Los Angeles coach Todd McLellan said.
Adrian Kempe and Phillip Danault scored for the Kings (41-27-10), who have won two straight and three of four.
Los Angeles moved two points back of the Edmonton Oilers for second in the Pacific Division and extended its lead over the Vegas Golden Knights and Vancouver Canucks to five points. The Canucks lost 4-3 in a shootout to the Ottawa Senators on Tuesday.
"If we expect to play a couple of weeks from now, we have to be comfortable [in one-goal games]," Quick said. "Especially this time of the year, these games are more frequent."
Adam Henrique scored, and John Gibson made 26 saves for the Ducks (30-34-14), who have three wins in their past 20 games.
"When I think of the Kings-Ducks rivalry, I think of Gibson and Quick," Anaheim coach Dallas Eakins said. "I thought they were both going at it. It was very reminiscent of battles of the past. I thought Quick was very good, and 'Gibby' was right there matching him."