Miles Wood, Blake Coleman and Jesper Bratt scored for the Devils (9-10-4), who have lost three games in a row and are 2-9-1 on the road. Sami Vatanen had two assists, and Keith Kinkaid made 30 saves.
Florida ended a three-game losing streak. It was coming off a 5-4 overtime loss to the Chicago Blackhawks on Saturday after allowing the tying goal with 1.8 seconds left in the third period.
"I thought we probably should have won the last game here at home vs. Chicago, but unfortunately those things happen," Hoffman said. "It's a long season, but it's in the past. We can't really do anything about that. It all depends on how we respond, and getting the win here tonight, it's big."
The Devils are 0-4 in overtime.
"We've got to keep working at it," coach John Hynes said. "It's been different situations, different guys, different things. When you look at it, there's not one particular trend. The last couple of games, we lost the first face-offs; tonight, we won the first face-off, had possession. We'll continue to work at it."