Filip Forsberg scored twice for the Predators (24-19-7), who won 5-4 at the Washington Capitals on Wednesday. Forsberg and Matt Duchene scored in the shootout.
"You kind of hit rock bottom and now we're coming on the way up and I know our best is yet to come," Duchene said. "We're working and we should feel great about these past two wins and bring that enthusiasm, that confidence and that swagger into Saturday (against the Vegas Golden Knights)."
WATCH: [All Predators vs. Devils highlights]
Pavel Zacha had two goals and an assist for the Devils (18-24-8), who led by one goal three times.
"It was my first time playing against someone who coached me in the NHL," Zacha said. "It was a challenge as it is every game. But this was a little special and you could see it was a high-paced game."
Duchene scored on a wrist shot from the left circle 33 seconds into the third period for a 4-4 tie. John Hayden scored to give the Devils a 5-4 lead at 6:37, and Forsberg made it 5-5 with a power-play goal at 9:57.
"The effort is what stuck out to me the past two wins," Forsberg said. "There are times when we've been down a couple of goals going into the third and we just quit playing. I think that's the biggest thing ... just our mentality. The belief is back, a little bit, and it's showing."