Thornton and Cheechoo also assisted on Curtis Brown's opening goal, and Evgeni Nabokov stopped 20 shots in another strong home start as the Sharks snapped a two-game losing streak with their sixth victory in eight games.
San Jose took a two-goal lead in the first period and hung on to win a matchup of two top Western Conference teams who met in the first round of last season's playoffs. Nashville hasn't won in the Shark Tank in four years.
Josef Vasicek scored his first goal since opening night for the injury-plagued Predators, who wrapped up a West Coast road trip with their fourth loss in five games. Chris Mason made 23 saves, but Nashville struggled to score while playing without several injured regulars - including high-scoring forward Steve Sullivan, who sat out with a strained groin.
Cheechoo, who led the NHL with 56 goals last season, scored late in the first period before adding his 10th of the season during a two-man advantage in the final minutes of the third. Cheechoo, who also connected with Thornton two nights earlier to snap a monthlong goal drought, now has scored in consecutive games for the first time all season.