Martin Erat, Sergei Kostitsyn and Mike Fisher also scored for Nashville, which won its fourth straight.
Rookie Sean Couturier and Wayne Simmonds had Philadelphia's goals as the Flyers snapped a two-game win streak.
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.
Nashville regained its two-goal advantage at 4:30 of the third when Jordin Tootoo's centering pass deflected off of the shaft of Spaling's stick and past Flyers goalie Ilya Bryzgalov.
Simmonds pulled teh 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.
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.
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.
NOTES: 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.
