The Rangers scored two goals in the second period and another in the third to move up from ninth place to seventh in the Eastern Conference. New York fell out of a playoff position for the first time this season with a loss at Carolina on Monday.
Tortorella, who benched forward Nikolai Zherdev for the rest of the game after his first-period turnover led to a goal, refused to reveal what he told his players.
Scott Gomez, who scored the tying goal for the Rangers and helped set up two others, said the message was an eye-opener. The Rangers are 4-2-1 since Tortorella replaced fired coach Tom Renney.
"He wasn't happy after the first period," Gomez said. "It has been a while since I've heard a speech like that. We were playing too timid. Nashville had the 2-1 lead and we thought it was over.
"He let us know what it is going to be like from now on. He lit into all of us. We were feeling sorry for ourselves and he spotted that right away. He called us out. I thought we responded well."
Henrik Lundqvist, who sat out Monday's loss because of a stomach ailment that has bothered him for about 10 days, stopped 19 shots for his 30th win of the season. He is the first to win 30 games in his first four seasons and the first Rangers goalie to do in any four-season stretch.
"It is a great feeling to be part of history," Lundqvist said. "The first four years have been great. When I look back on my career I will definitely think about this accomplishment. Part of this is because of my teammates, as well."
Lundqvist also was inspired by Tortorella's talk.
"He let us know how we should play and how we should have played in the first period," he said. "It is pretty obvious to us that when we get more involved, play more physical and go after teams that we are a better team.
"That is what we started doing in the second period. We made it a lot tougher for them to create chances and get confidence."
Sean Avery scored his first goal since being picked up by the Rangers off waivers last week from the Dallas Stars.
The Rangers peppered goalie Dan Ellis, who made his second consecutive start, with 32 shots.
"They started taking it to us a little bit more in the second period, and we never really recovered from it," Ellis said. "They came with a lot of pressure. That's what the scouting report was on them - that they were going to come at you no matter where you were on the ice."
Avery scored his fourth goal overall. Marc Staal and Fredrik Sjostrom added goals for New York.
Shea Weber and J.P. Dumont netted the Predators' goals.
Avery gave the Rangers a 1-0 lead 3:38 into the first period. Gomez's shot bounced off the back boards and the puck slid across the crease. Avery skated in from the right side and tapped it into the open side of the net to beat Ellis.
Weber tied it with nine minutes left in the period with a power-play goal as he fired a wrist shot from a few feet inside the blue line. The puck bounced off Lundqvist's glove and into the net.
Dumont gave the Predators their first lead with 5:06 remaining in the first. He tried to center the puck from the left circle but his pass bounced off the skate of Rangers defenseman Dan Girardi and into the net.
The Rangers made it 2-2 at 3:01 of the second period. Ellis cleared the puck from behind the goal, but Ryan Callahan intercepted the pass and fired a shot from the left side. Gomez got position in front and directed the puck into the net.
The Rangers took a 3-2 lead with 2:31 left in the second. With several players scrambling for a rebound in front of the net, Staal tapped the puck past Ellis.
Sjostrom added a short-handed goal 7:59 into the third period.
Notes: Weber's 18th goal tying the franchise record for most in a season by a defenseman. ... Ellis made his first career start against the Rangers. ... Tortorella replaced Renney on Feb. 23.
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