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.
"They have a lot of firepower and they seem to create a lot of those chances off the walls and behind the net," Rinne said. "They are really creative guys who play well together, but we did a really good job for the most part of shutting them down."
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.
"It definitely feels good," Fisher said. "I've been out for a long time, but fortunately I have been able to skate a lot and get my legs going. I've been the recipient of some great plays too and that helps a lot."
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.
"We got 2-0, and then we turned a couple of pucks over and got them a lot of chances," Nashville head coach Barry Trotz said. "At 2-2, you sort of test your resiliency there."
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.
The Lightning had a strong start to the second, but were unable to capitalize on any of their chances and felt the Hornqvist goal hurt their momentum.
"The first six or seven minutes we were all over them and then they got the goal," Lighting head coach Guy Boucher said. "That third one hurt because of the circumstances; playing so well, not being able to score, and having momentum."
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.
"I've got to make some saves," Garon said. "If I make a couple of more saves, it's a different game. I've got to be better than that."
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. Following the game, Trotz said that the injury was not believed to be serious and that the team was optimistic he would be available for the team's next game on Saturday.
Stamkos' team-leading sixth goal of the season came at 17:03 of the third.
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.