Rookie Sean Couturier and Wayne Simmonds had the goals for the Flyers, who snapped a two-game win streak. Philadelphia is winless in its last five trips to the Music City, with its last victory coming March 21, 2000.
Trailing 2-0, Couturier cut the deficit in half with 7:42 to go in the second period with a slick wrist shot from the right circle that beat Rinne high to the glove side and tucked just underneath the crossbar. Couturier's score gave him a goal in four straight games.
"I thought our guys got the attempts," Flyers coach Peter Laviolette said. "We turned things back in the direction we wanted, and we didn't get the results. You play a couple of games and get wins, but you want a better process though it, and tonight, the process was a bit better."
Nashville regained its two-goal advantage at 4:30 of the third when Jordin Tootoo's centering pass deflected off the shaft of Spaling's stick and past Flyers goalie Ilya Bryzgalov.
"It was a lucky bounce, but I will take it," Spaling said. "Our game plan is to go to the net and funnel the pucks there. That's the way we want to keep playing."
The goal was Spaling's third game-winner this season.
Simmonds pulled the Flyers to 3-2 at 9:55 as he outmuscled Nashville defenseman Ryan Ellis to get the rebound of Couturier's backhand shot from the left circle and then poked the puck past Rinne.
"It was kind of the same feeling all game; you were down one goal, you were down two goals," Simmonds said. "We are a resilient team and tried to come back, but we just couldn't come back tonight."
Rinne made 15 saves in the first, 12 in the second, and nine in the third to record his 23rd win of the season.
"Unfortunately they got that second goal and that gives a lot of energy to your team, but after that, they really didn't have anything," Rinne said. "They had a few chances here and there. We did a really good job defensively."
Fisher's empty-net goal with 39 seconds to go sealed the Predators' win.
Erat gave Nashville a 1-0 lead with 57.7 seconds remaining in the opening period. From the right circle, Erat's wrist shot bounced in front of Bryzgalov before skipping over the goalie's right shoulder. Nashville's Patric Hornqvist was just outside of the goal crease providing a screen for Erat's shot, which gave him a goal in five of his last six games against the Flyers.
"We had some good looks in the first period, and the funny thing was we had all the good looks and some great chances, and the one we scored on wasn't a particularly great chance," Nashville coach Barry Trotz said. "It was a seeing-eye puck. (Hornqvist) did a great job on screening Bryzgalov and Marty just sort of put it there."
Kostitsyn made it 2-0 at 10:36 of the second. Just 10 seconds after a penalty to Philadelphia's Brayden Schenn expired, Kostitsyn's wrist shot from the high slot through traffic beat Bryzgalov high to the glove side.
Nashville rookie C Craig Smith missed his first game of the season due to a flu-like illness. ... Fisher has points in four consecutive games. ... Simmonds has points in three-straight games. ... The Flyers are 7-2-2 against the Western Conference this season with both regulation losses coming against Central Division teams.