Thornton also scored the tying goal early in the third period and Evgeni Nabokov made 23 saves, including a handful of jaw-dropping stops, as the Sharks earned a point in their 17th consecutive game. They're six points ahead of second-place Anaheim with a game in hand on the Ducks, who host the Sharks on Friday night.
San Jose needs three points from its last five games to clinch the third division title in franchise history and a No. 2 seed in the Western Conference playoffs.
Captain Brenden Morrow and Jere Lehtinen scored for the falling Stars, who lost for the eighth time in nine games and finally lost any mathematical chance of winning the division they led just a few weeks ago.
Marty Turco made 24 saves but took a four-minute high-sticking penalty early in overtime, eventually leading to Thornton's score. Captain Patrick Marleau appeared to think he had deflected home Thornton's pass in a crowd in front of Turco, but several minutes after Marleau took a bow in front of the sellout crowd, the official scorers awarded the goal to Thornton, the NHL assists leader who has seven goals in five games.
Turco slashed Joe Pavelski across the face with his stick just 75 seconds into overtime, but Mike Modano missed a shorthanded scoring chance moments later when his attempt to stuff the puck across the goal line improbably was stopped by Nabokov's stick. Modano, who jokingly dubbed his team "the San Jose Stars" on its last trip to the Bay Area, had two assists.
Pavelski scored an early goal for the Sharks, who have won 15 of their last 17 games. They haven't lost in regulation since Feb. 20.
Lehtinen put the Stars ahead 2-1 during a two-man advantage in the second period, but Thornton tied it early in the third when Mike Grier did his best Thornton impression, flipping a cross-ice, no-look backhand pass to the Sharks' leading scorer.
The Sharks played their second straight game without goal-scoring forward Jonathan Cheechoo, who's still recovering from a hit to the head in last Friday's win over Anaheim. Cheechoo isn't expected to miss much more time, but Jeremy Roenick took his place on the Sharks' top line with Thornton and Milan Michalek.
Defenseman Philippe Boucher returned to the Stars' lineup after missing six games with a right shoulder injury.
