Carolina outshot Nashville 24-7 in the first period.
"It's probably one of the best periods I've seen ever," Hurricanes coach Rod Brind'Amour said. "Probably should have had a few more, but it was nice to get one at least."
Josi tied it 1-1 at 11:36 of the second period. He intercepted a clearing attempt by Carolina defenseman Jake Bean and skated into the slot before scoring with a turnaround shot over the glove of Nedeljkovic.
"I thought we played better in the second and the third," Josi said. "Saros really kept us in there. He did an amazing job."
After Hakanpaa gave Carolina the lead, Andrei Svechnikov scored an empty-net goal with 1:51 remaining in the third period.
Predators forward Matt Duchene had two shots and three hits in 14:46 of ice time after missing 22 games with a lower-body injury.
"Fortunately, I was able to skate pretty hard, but I wasn't battle-ready for a while," Duchene said. "It was good to feel good out there, but it would feel a lot better with a win tonight."
NOTES:Predators defenseman Erik Gudbranson, who was acquired in a trade with the Ottawa Senators on Monday, had one shot and three hits in 15:40 of ice time in his Nashville debut. … The Predators lost consecutive games for the first time since they lost three in a row from March 9-13. … Josi has scored four points (two goals, two assists) in his past three games ... The Hurricanes, whose 48 shots were a season high, have outscored the Predators 23-9 this season. They finished their season-long eight-game homestand 5-2-1.