Nashville forward Steven Stamkos tied the game 2-2 at 19:59 of third period when he buried a wrist shot from the top of the left face-off circle.
Will Smith and Mason Marchment scored for the Sharks (4-3-0), who had lost three of their past four games.
“For the most part, I liked a lot of our game,” San Jose coach Ryan Warsofsky said. “I thought there was some improvement in some areas. There are still areas to work on, but we’ll take the two points and move on.”
Ryan O'Reilly also scored for the Predators (2-2-3), who have lost four of their past five (1-1-3). Saros made 30 saves.
“We’re a resilient group,” Nashville coach Andrew Brunette said. “You kind of felt the tide turning there in the last 10-12 minutes of the (third) period. We were hoping for one last look, and we got one. 'Stammer' did Stammer things. It was a big goal. It would’ve been nice to put the game away, both teams in overtime had chances. … They’re coin flips when we get to that spot in the game.”
Tyler Toffoli’s no-look pass from below the goal line to Marchment gave the Sharks a 1-0 lead at 5:30 of the first period. Toffoli corralled a loose puck behind the net and fed a pass to Marchment in the slot, where he sent a one-timer past Saros.