Marc Staal and Fredrik Sjostrom each had a goal while Henrik Lundqvist stopped 19 shots for the Rangers, who have won four of their last five games.
Sean Avery scored his first goal since rejoining New York last week.
Shea Weber and J.P. Dumont each had a goal for the Predators, who have dropped their past three games on the heels of a six-game winning streak. Dan Ellis stopped 28 shots in the loss.
The Rangers jumped out to a 1-0 lead at the 3:38 mark of the first as Gomez threw a pass from the left side to the right where Avery reached out and tapped the puck in.
Nashville, though, scored twice in a span of 3:56 to take a 2-1 lead.
Weber tied the game at the 11-minute mark as his wrister knicked off the glove of Lundqvist and crossed the goalline for a power-play tally.
On the rush, the Predators took a 2-1 lead as Dumont's pass from the left side was kicked into the net by New York's Dan Girardi.
New York tied the game at the 3:01 mark of the second as Ryan Callahan shot from the left side was tipped in by Gomez in front of the net.
Late in the second period, the Rangers took a 3-2 lead. Avery skated through the slot and threw a shot on net from the right circle that was tipped off the right post. With several players battling in the crease, Staal slammed the puck home with 2:31 left in the frame.
Skating shorthanded, New York took a 4-2 lead on a 2-on-1 break as Blair Betts slid the puck from the left side to the right where Sjostrom wristed it home at the 7:59 mark of the third.