Kieffer Bellows broke a tie early in the third period, and Steven Stamkos also scored for the Predators (25-32-7), who have won four straight and five of seven. Juuse Saros made 25 saves.
"It was tough sledding,” Nashville coach Andrew Brunette said. “We worked really hard and they are a fast team. We probably managed things very good for most of the game. The power play was big, and [Saros] was the same."
Patrick Giles scored his first NHL goal, and Collin Graf also scored for the Sharks (17-40-9), who have lost three in a row. Alexandar Georgiev made 16 saves.
"I actually liked our game; [we had] some good chances," San Jose coach Ryan Warsofsky said. "The penalties just take momentum away from our group and the flow of the game."
Forsberg gave the Predators a 1-0 lead with a power-play goal at 8:11 of the second period. After curling around the bottom of the right face-off dot, Forsberg scored on a wrist shot over Georgiev's glove.