Kopitar's goals were his first of the season for Los Angeles, which had gone 0-2-1 in the first three contests of the lockout-shortened campaign.
Jake Muzzin helped out with a goal and an assist and Jeff Carter added a goal for the Kings.
Jonathan Quick earned the victory with 32 saves.
Phoenix has lost four of its first five contests.
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Aaron Carter is still in love with Hilary Duff