Fisher's two goals lifts Nashville over Tampa Bay
Sergei Kostitsyn, Patric Hornqvist, and Nick Spaling also scored for Nashville. Steven Stamkos had two goals and Teddy Purcell had one for the Lightning.
The victory gave the Predators their first home win of the season in their fourth attempt. Tampa Bay saw its three-game winning streak end.
Pekka Rinne, who has started every game in goal for Nashville this season, made 29 saves to record his fourth victory of the season and 99th of his career.
Fisher appeared in just his second game of the season, as recovery from offseason shoulder surgery caused him to miss Nashville's first seven contests.
He has four points in his two games played.
After Kostitsyn and Fisher gave the Predators a two-goal lead in the first, Stamkos and Purcell answered back late to send the teams into the first intermission tied 2-2.
Purcell's power-play goal came with just 27 seconds remaining in the first.
Hornqvist's first goal of the season came at 7:43 of the second period on a tap-in from the low slot. He has been bothered by an injury to his right foot for most of the young season.
Spaling and Fisher scored goals 50 seconds apart midway through the second, spelling an early end to Mathieu Garon's night in the Tampa Bay goal.
Garon stopped just 12 of the 17 shots he faced in 32:10 played. He was replaced by Dwayne Roloson.
With just under 12 minutes elapsed in the second period, Kostitsyn was hit by Tampa Bay's Brett Connolly in the right corner of the Nashville zone. Kostitsyn spun and went into the corner boards awkwardly with his left leg twisting as he fell.
Kostitsyn did not return to the game, but a Predators' team official said the injury was not believed to be serious.
Stamkos' team-leading sixth goal of the season came at 17:03 of the third.
Notes: Purcell played in his 200th career NHL game. ... Garon's career record against Nashville is now 2-8-2. ... Dating back to December 15, 2009, the Predators have defeated Tampa Bay three consecutive times The five goals scored are a season-high for Nashville.