Saros made four saves in the shootout for the Predators (22-10-1), who have won three consecutive games, five of their past seven, and lead the Western Conference with 45 points.
"It feels good," Saros said. "It was a nice game from a goalie's standpoint. I saw a lot of pucks and a lot of shots from outside, so I felt good."
WATCH: [All Devils vs. Predators highlights]
Brian Boyle scored, and Keith Kinkaid made 27 saves for New Jersey (11-13-7), which is 3-11-3 on the road.
"Keith played really well," Devils coach John Hynes said. "I think this was a game where we got good goaltending but we felt we were the better team. I mean we had a lot of chances. I thought we carried the play, we were defensively sound. When we needed saves Keith was fantastic, and that's what you need.
"We don't feel like we stole a point. We feel like we didn't get the second [point], and that's the difference. Sometimes you can get outplayed and you can steal a point. Tonight we didn't steal a point. Tonight we didn't get the second one."
Boyle tied the game 1-1 with 1:31 remaining in the third period on a rebound in the slot. Marcus Johansson took the original shot, and Boyle scored on the rebound for his ninth goal.