Josi took a pass from Mikael Granlund and beat goalie Malcolm Subban on the forehand for his first goal of the season.
"I saw some space," Josi said. "[Granlund] made a good play down low. He dropped it to me, and I saw that I had some space, and from there I was thinking about just taking it to the net and making a move on the goalie. Luckily it went in."
The Predators (3-3-0) ended a three-game losing streak, including two straight at the Dallas Stars. Pekka Rinne made 18 saves for his first win since Feb. 16, 2020.
The teams play again here Wednesday (7:30 p.m ET; NBCSN).
"It was a gutsy win," Rinne said. "It was big for us. Obviously, a disappointing trip to Dallas (two losses), even though we felt like we played fairly well. Obviously, it was a disappointing outcome, especially the first game (7-0 on Friday). Crucial win for sure. It's a back-to-back, huge points, and every game is so important right now. Just the way we played tonight, I thought that it was a full 60 minutes and overtime. We continued pressing. We were attacking the game and doing a lot of the right things, so you've got to give a lot of credit to the guys for sticking with it and playing hard."