Subban gave the Predators a 1-0 lead 19 seconds into the second period on a one-timer from the top of the right face-off circle. Filip Forsberg retrieved the puck behind the net and gave Subban a backhand feed, and he beat Lundqvist for his 13th goal.
Peter Holland appeared to tie the game 1-1 at 10:14 of the second period but the Predators challenged the play for offside and the goal was overturned on video review.
Fiala made it 2-0 at 17:34 on a wrist shot from the slot. Craig Smith corralled a misplayed puck by Rangers defenseman Brady Skjei and found Fiala, who beat Lundqvist for his 14th goal.
Miller scored 21 seconds into the third period to make it 2-1 when he redirected a pass from the point by Mats Zuccarello for his 12th goal.
The goal ended Rinne's shutout streak at 171:46.
Colton Sissons gave the Predators a 3-1 lead at 2:36 of the third period on a redirection of a shot from the point by Subban. It was his fifth goal.
"It always feels good," Sissons said. "It felt like no matter what I tried to do out there, I couldn't find a goal for a while. So hopefully this thing keeps rolling."
Zibanejad cut the lead to 3-2 at 14:35 on a one-timer from the point.
Viktor Arvidsson scored 16 seconds later to give the Predators a 4-2 lead. It was his 17th goal.
"When you've got guys like [Forsberg], [Ryan Johansen] and [Arvidsson] that have everything that you want in a top line on your team with physicality, speed, skill, you've just got to be aware when they're on the ice," Subban said. "For them to go out and execute like that right after those goals is pretty big for our team."
Fiala scored into an empty net on the power play at 17:56 to make it 5-2.
