Arvidsson has scored five goals in his past four games.
"I think I've played fast a lot this year," the forward said. "I think I've made better reads so I can get loose, getting behind the [defense] sometimes and making reads that my [defensemen] are able to make the plays. I think the speed has been there. It's just trusting my [defensemen] and trusting my reads."
Roman Josi scored three points (one goal, two assists), and Tanner Jeannot scored his first NHL goal for the Predators (24-19-1), who have won 13 of their past 16 games. Juuse Saros made 21 saves.
"We started really well," Josi said. "We got a couple of goals, [and] obviously that helps. I thought they made a push in the second and were the better team for most of the second, but [Saros] was great. He made a lot of huge saves. I liked our response in the third. It's a big win for us against a really good team."
Brayden Point scored for the Lightning (28-12-2), and Curtis McElhinney made 15 saves.
Nashville scored three goals in the first period and in the third.
"I don't care who is in net, ever," Lightning coach Jon Cooper said. "You can bring back Dominik Hasek or Marty Brodeur or Patrick Roy, nobody is stopping the chances we gave up tonight."
David Savard made his debut with Tampa Bay being traded by the Columbus Blue Jackets on Monday. The defenseman, who was paired with Victor Hedman, was minus-4 in 19:23 of ice time.
Colton Sissons gave the Predators a 1-0 lead at 6:38 of the first period with a wrist shot from the left circle. Josi made it 2-0 lead at 8:31 with a wrist shot from the right circle.
"I think confidence a lot of times is earned through hard work," Josi said. "You've got to put in the work, and that's when you get the bounces and that's when the confidence gets bigger and bigger. I thought we did that in the last little while here. I think our work ethic is the biggest part. That's how we're getting bounces and that's how we're gaining confidence."
Arvidsson gave Nashville a 3-0 lead at 13:50 of the first on a 2-on-1 with Ryan Johansen.