Thornton's power-play tally on assists from Joe Pavelski and Dan Boyle 6:09 into the game set the tone for the Sharks, who came into the contest trailing 3-2 in the Western Conference semifinal series.
T.J. Gallardi doubled the advantage early in the second period with his first post-season tally.
Antti Niemi assisted on Galliardi's goal and turned aside 24-of-25 shot for San Jose, which will now face the Kings in a winner-take-all deciding game Tuesday at Staples Center.
Dustin Brown scored in the middle frame for Los Angeles, which was coming off a 3-0 victory in Game 5.
Jonathan Quick made 24 saves for the Kings.