Quick's busiest period was the second, when he stopped 9-of-10 shots and helped the Kings to their third straight win and fifth in six contests overall.
Carter's tally late in the initial frame put Los Angeles ahead 2-0.
Dustin Brown, Trevor Lewis and Anze Kopitar also scored for the Kings.
The Avalanche captain assisted on Hejduk's goal.
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Aaron Carter is still in love with Hilary Duff