William Eklund scored for the Sharks (16-46-7), who have lost six games in a row. Mackenzie Blackwood made 17 saves in his first start since Feb. 27.
"I really liked our first two periods," San Jose coach David Quinn said. "I thought we managed the puck really well, defended hard. We played a really good game."
Nicholas Paul put Tampa Bay ahead 1-0 at 4:53 of the first period. Victor Hedman's pass skipped over the net and set the center up for a wrist shot up close.
Eklund tied it 1-1 at 7:21 after Jacob MacDonald intercepted a pass in the neutral zone and set Eklund up with a cross-ice pass.
"I haven't played my best hockey here, but I think today was a huge step in the right direction," Eklund said. "You're not always going to have ups in a season, you're going to have some downs. I'm learning here, and I'm going to keep learning and be better."