Subban recorded his 10th multi-point game by scoring the game's first goal on a one-timer 19 seconds into the second period and setting up Colton Sissons' goal early in the third period.
Nashville improved to 8-1-1 in its past 10 games.
Predators goalie Pekka Rinne saw a lengthy shutout streak end but got the win with 20 saves.
J.T. Miller and Mika Zibanejad scored power-play goals for the Rangers, who are 4-8-0 in their past 12 games.
Already playing without Pavel Buchnevich (concussion), the Rangers also lost defenseman Marc Staal and Jimmy Vesey to apparent head injuries in the second period.
Nashville took a 1-0 lead early in the second period when Subban scored his 13th goal of the season. Subban fired a one-timer over Lundqvist's shoulder after the Predators kept possession of the puck and Filip Forsberg whipped a pass to him from behind the net.
The Rangers appeared to tie the game on a goal by Peter Holland with 9:47 left in the second. Nashville used its coach's challenge, and replays showed Michael Grabner's left skate was offside when he made the pass to Holland.
Nashville doubled its lead when Fiala capitalized on a turnover by New York defenseman Brady Skjei. Fiala converted a wrist shot from the low slot over Lundqvist with 2:26 remaining.
Miller scored 21 seconds into the third by redirecting a pass from Mats Zuccarello. The goal ended Rinne's shutout streak at 171:47.
Nashville regained its two-goal lead shortly after a turnover by Rangers defenseman Brendan Smith. Moments after Smith's errant clearing pass in the defensive zone, Subban gained possession and unleashed a long drive from beyond the left circle, and Sissons redirected it over Lundqvist's right shoulder.
The Rangers made it a one-goal game again at 5:25 when Zibanejad fired into the upper right corner of the net. However, Arvidsson scored on a wrist shot from the left circle 16 seconds later, moments after a New York defensive miscue.
The Rangers pulled Lundqvist with 3:22 remaining, but 38 seconds later, Subban drew a holding penalty on Grabner. With 2:05 to go Fiala scored into the empty net, his 15th of the season.
--Field Level Media
NY Rangers | Nashville | |
J.T. Miller 2 | Points | Kevin Fiala 2 |
J.T. Miller 1 | Goals | Kevin Fiala 2 |
Ryan McDonagh 2 | Assists | Filip Forsberg 2 |
J.T. Miller 1 | Power Play Goals | Kevin Fiala 1 |
N/A | Short Handed Goals | N/A |
Henrik Lundqvist .852 | Save Percentage | Pekka Rinne .909 |
Henrik Lundqvist 23 | Saves | Pekka Rinne 20 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
NY Rangers | 22 | 2 | 2-3 | 4-5 | 17 | 29 |
Nashville | 28 | 5 | 1-5 | 1-3 | 13 | 37 |