The Sharks won the season-series 3-2-0 and defeated the Kings at SAP Center for the first time in three tries.
"We've been playing some good hockey, we just haven't clinched," Thornton said. "To finally get that out of the way. Now just keep playing hard and stay healthy."
Vincent Lecavalier scored two goals for the Kings (45-26-5), and Jonathan Quick made 26 saves.
The Kings' lead in the Pacific Division over the second-place Anaheim Ducks, who defeated the Edmonton Oilers 2-1, is one point. San Jose trails the Kings by five points.
"We had so many opportunities to get goals," said Kings defenseman Drew Doughty, who played his 600th NHL game. "We should have won the game. We didn't get that go-ahead goal. Jones played well in the net for them. They got a couple of lucky bounces especially at the end especially after we tied it up at [2-2]. We might see them in the playoffs. We showed them that we'll be a tough match for them."