Tampa Bay had dropped five of its first seven games of the season. The Lightning's seven-season losing streak against the Sharks had covered five games.
James Wright, Ryan Malone and Andrej Meszaros also scored for Tampa Bay, which owned a 2-0 lead after one period and had a 3-1 advantage after two.
Evgeni Nabokov took the loss, stopping 20 of 24 shots.
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