The Sharks' third win in the fifth of a six-game homestand provided a confidence boost after they put themselves in an early-season hole.
"We all knew we weren't playing up to our standards, and kind of forgot how the game is played a little bit for a while," defenseman Erik Karlsson said. "It feels like we're finally starting to look like the team we're supposed to be. Still a long way to get there where we want to get, but this is a good start."
Tomas Hertl tied the game 1-1 for San Jose at 5:22 of the third period when he scored on the rebound of Meier's redirection of Marc-Edouard Vlasic's shot from the left point.
"I thought he was excellent," Sharks coach Peter DeBoer said of Hertl. "Actually, we didn't have any passengers tonight. I thought everybody showed up and gave us a real good game, but he was exceptional.
The Predators had a power play for the final 1:31 of overtime after Evander Kane was called for hooking Mikael Granlund, but Jones made four saves.
San Jose killed all four Nashville power plays and has the best penalty kill at home in the NHL (30-for-31, 96.8 percent).
"Specialty teams, even though we didn't score on the power play, were all good out there, and we created a lot of momentum that carried through on the 5-on-5," Karlsson said. "For the most part, it felt like we were carrying this game."
Filip Forsberg fought off Karlsson and scored with a high wrist shot at 14:44 of the second period to give the Predators a 1-0 lead.