Kopitar's goal, his second of the season, came with San Jose's Justin Braun in the penalty box for hooking.
The Sharks lost for only the third time in 13 games this season with two of those setbacks having come in overtime.
Los Angeles faced a 3-2 deficit heading into the third period, but Justin Williams scored on the power play with 7:39 to go in regulation. It was the third time the Kings had overcome a one-goal deficit.
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