Bonino gave the Predators a 5-3 lead at 5:47 of the third period on a wrist shot from below the left circle. Taylor Hall scored for the Devils to make it 5-4 at 11:09 on a rebound of a shot by Jack Hughes.
Grimaldi gave the Predators a 6-4 lead at 12:44 of the third period on a breakaway after getting by Subban at the opposite blue line.
"[Mattias Ekholm] rimmed it around, and I didn't think I was going to get there," Grimaldi said. "I thought whoever the [defenseman] was, I didn't know it was [Subban] at the time, I thought he was going to get there first because I was a little behind it. He might have slowed up a little bit because of the snow, he made a move, I chipped it by him and thankfully it got by him. I went on a breakaway and scored."
Daniel Carr gave the Predators a 1-0 lead 46 seconds into the first period with his first goal of the season, and Fabbro made it 2-0 at 2:13 on the rush.
"I think there's always things you can improve on, but I like the way guys battled through little things," Fabbro said. "I don't think you want to give up a lead like that, but we found a way to get back on top and finish the job."
Jesper Bratt scored to make it 2-1 at 2:45 on a shot from the slot on a pass from Pavel Zacha, and Travis Zajac tied it 2-2 at 3:59.
"We fought our way back," New Jersey forward Kyle Palmieri said. "That's maybe one positive you can bring out of it, but there were plays to be made that we didn't execute tonight. We were sloppy in some of the decision-making we had."
Yakov Trenin gave the Predators a 3-2 lead at 5:52 of the first period on a redirection of a shot by Grimaldi. It was Trenin's first NHL goal in his second game. Filip Forsberg made it 4-2 lead at 7:24 off a rebound.
Palmieri scored to make it 4-3 at 13:07 on a one-timer from the slot off a pass from Hall.
Subban was traded by Nashville to New Jersey on June 22. He had one shot attempt in 18:20 of ice time and was not available to the media after the game.