Filip Forsberg put Nashville ahead 3-2 at 7:02 of the third when he scored on a wraparound, banking the puck off Sharks defenseman Tim Heed's skate.
Arvidsson scored into an empty net at 18:54 for the 4-2 final. The goal was his 31st in 49 games and tied his NHL career high (2016-17).
"It's a crazy year," said Arvidsson, who missed 21 games with a broken thumb. "An injury and stuff like that. I think I started good and got going pretty good at the beginning of the year, then got injured. Then it's just been going really good. [Ryan Johansen and Forsberg] have been unreal, setting me up and giving me passes."
Colton Sissons gave Nashville a 1-0 lead at 1:07 of the first period when he took pass from Craig Smith and scored from close range on an odd-man rush.
"I think we expended a lot of energy in trying come back into that game," DeBoer said. "I thought we were chasing it a lot of the night, which is unfortunate. They got the first goal, obviously, and then you're chasing it, then down 2-1 and you're chasing it, so you spend a lot of energy doing that and I think that probably caught up to us a little bit."
Meier tied it 1-1 at 4:09 of the second period with his 27th goal of the season. He took a cross-ice pass from Joe Pavelski and scored on a wrist shot from the right circle.
Arvidsson made it 2-1 24 seconds later when Forsberg's shot from the left circle deflected off Arvidsson's right ankle at 4:33.
Joe Thornton scored from the low slot on a give-and-go with Brent Burns at 17:36 to make it 2-2.
"We know how good San Jose is," Predators coach Peter Laviolette said. "They were here to clinch their spot tonight. For us to come in against a real good team from the other division, I thought it was really strong for our guys.
"I thought we played a complete 60 minutes. Good responses too when they scored we were able to score right back again, which I thought was important, and then to get the lead in the third as well."
Sharks forward Evander Kane returned to the lineup after missing seven games with a mid-body injury and skated on the second line with Tomas Hertl and Gustav Nyquist. Kane was away from the team for five days to be with his wife after a miscarriage. He had three shots and three hits in 19:44.
"He did a good job," DeBoer said. "Considering what he's been through, the fact that he even got out here today was very impressive. He gave us everything he had."
