Lafreniere gave the Rangers a 2-1 lead at 10:53 of the third period on a rush with Sammy Blais. Adam Fox gave the puck to Blais in the offensive zone, and he passed to Lafreniere for the tap-in.
"I just like to be out there when the game is tight," Lafreniere said. "It was a good game tonight, really physical. In the third period, we knew what we had to do. Like I said, I like to be out there in big moments. It was a real good play by [Fox] and [Blais], and I was lucky enough to score."
Igor Shesterkin made 28 saves, and Blais had two assists for the Rangers (3-1-1). Each of their three straight wins has come on the road.
"Gritty, gritty effort tonight," New York coach Gerard Gallant said. "Tonight, for me, was the toughest game we've played so far this season. Everybody battled for ice, both teams. I thought Nashville was real good. I thought we competed hard. I thought it was a gritty, gritty game and we came out on top."
Philip Tomasino scored his first NHL goal for the Predators (1-3-0). Juuse Saros made 27 saves.
"We generated a lot of good chances and spent a lot of time [in the offensive zone]," Nashville coach John Hynes said. "Unfortunately they didn't go in tonight, but we've just got to figure out how we can capitalize on the chances. But I think when you're generating them and getting them there, I think that's the key. Now the next step is putting them in."
Filip Chytil gave the Rangers a 1-0 lead at 2:12 of the first period on a backhand shot after a pass from Blais.
"For sure, it gave us confidence," Blais said. "I think we scored on our first or second shift. … I think in the first, we were really good. I think we're three guys (Lafreniere, Chytil, Blais) that can play with the puck. When we use our speed, I think we're dangerous."