Matt Luff and Jeff Carter scored, and Tyler Toffoli had two assists for the Kings (13-18-2), who were 0-10-1 on the road since a 3-2 win against the Winnipeg Jets on Oct. 22.
"Good team effort, great goaltending," Kings coach Todd McLellan said. "You need all of those things to win, especially on the road."
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Derek Grant scored, and John Gibson made 25 saves for the Ducks (13-15-4), who were trying to win two in a row for the first time since Nov. 1.
"We were playing with a little more desperation," Grant said. "We got good control and some good looks, but their goalie played well and we couldn't get it done tonight."
Quick has saved 65 of 67 shots in his past two starts.
"Even the goal we scored, he still got a piece of it," Ducks coach Dallas Eakins said. "He was certainly on his game tonight."
Anaheim had a season-high 15 shots on goal in the first period, but the Kings scored the only goal at 18:31.
Matt Roy took a one-timer from the right point. Gibson saved Luff's tip, but the puck went to Toffoli to the right of the net. Toffoli's shot attempt went under a sprawling Gibson and through the crease to Luff, who scored into the open side for a 1-0 lead.