Eeli Tolvanen scored for the fourth straight game for the Predators (16-10-1), who have won four in a row, including the first three of a four-game road trip.
"I think over the course of the season we've had excellent goaltending, and our special teams have done well, and that's a good recipe to win," Predators coach John Hynes said. "But I think, first and foremost, is the competitive nature and the toughness of the group that has been a determining factor during the win streak."
Pavel Zacha and Yegor Sharangovich scored, and Mackenzie Blackwood made 24 saves for the Devils (10-10-5), who are 1-4-1 in the past six games.
Zacha gave the Devils a 1-0 lead on a wrist shot from the slot at 11:34 of the second period. Nico Hischier took on two defensemen behind the Predators net and kicked the puck to Jesper Bratt in the left-wing corner to set up Zacha's ninth goal of the season.
"I feel like we were skating well, had a pretty good first period, but we got a little bit loose in certain areas and they scored right away," Hischier said. "It's a tough one but we have to buckle up. Just little mistakes, those details we're talking about can cost us a game."
Josi scored his ninth on a wrist shot from the right face-off circle to tie it 1-1 at 13:11.
"It was an awesome pass by Philip Tomasino; he showed great patience," Josi said. "I was kind of alone in the slot and tried to go low blocker, but I think it went through his hands a little bit."
Josi finished with a game-high nine shots in 23:05 of ice time.
"It goes back to the fact [Josi's] a highly talented player, has great vision, sees plays that others don't," Hynes said. "He can execute plays that others can't, but he's very consistent in the way that he plays. He's extremely competitive and he can do it in multiple ways.
"It's nice to see him continue to grow and lead the team in playing the right way."
Tolvanen scored a power-play goal on a slap shot from the left face-off circle to give the Predators a 2-1 lead at 17:53.
"[Tolvanen's] got so much substance to his game," Hynes said. "Now he's found a different way to produce offense to where he's willing to get into the inside of the ice and he gets tipped goals and screen goals. That's another way for a young player that wants to be, and has the potential to be, a scorer in this league regularly ... finding different ways to be able to contribute.
"I love his talent, but I just love the character and the competitiveness of the player."