Justin Faulk's goal 23 seconds into the game gave the Hurricanes a 1-0 lead, but it took a second-period rally for Carolina to leave Nashville with a win.
Mike Fisher tied the game when he tipped defenseman Victor Bartley's slap shot past Carolina goalie Justin Peters 50 seconds into the second period, and Viktor Stalberg gave the Predators a short-lived lead 1:51 later when his backhander on a rebound of a Nick Spaling shot snuck past Peters and inside the left goal post.
Carolina responded with four unanswered goals, including two in the second period by Skinner, who sealed the game with an empty-netter with 2:07 left in the third period.
Faulk scored his second of the season on the game's first shot, a wrister from the right wall that beat Nashville goalie Marek Mazanec under his glove. The teams combined for nine first-period shots.
Skinner tied it 2-2 at 6:11 of the second period. The Hurricanes left wing beat Mazanec under his glove with a wrist shot from the right faceoff circle for his seventh goal of the season.
Carolina (12-12-5) took the lead when Riley Nash scored on the power play with a wrist shot through Mazanec's five-hole at 11:51. It was Nash's second goal of the season.
The Hurricanes were 1-for-5 on the power play, including an unsuccessful 5-on-3 midway through the third period.
Skinner's slap shot from the right circle with less than 52 seconds left in the second extended Carolina's lead to 4-2.
The empty-net goal gave Skinner his first career hat trick.
"It's nice. I've had a couple two-goal games but I couldn't seem to find the third one," Skinner said.
Skinner has five goals in his past two games -- he scored two in a 4-1 win against the Washington Capitals on Tuesday. Hurricanes coach Kirk Muller hopes his fourth-year forward has rediscovered the scoring touch he had when he scored 31 goals as a rookie.
"I don't know how many shots he had on net tonight, but he can score when gets those opportunities," Muller said, according to The SportsXchange. "He's working for it."
Skinner impressed the Predators.
"He's a dynamic player," Bartley said, according to The SportsXchange. "He will shoot off the rush and shoot when he's turning. You really have to be on your game to try to block shots against him."
Peters made 20 saves for his third win in his past five starts.
Carolina lost three players to injury Thursday. Defenseman Mike Komisarek left the game in the first period and forward Drayson Bowman early in the third, each with a lower-body injury. Forward Patrick Dwyer took one shift in the third period after taking a high stick to the face from Stalberg late in the second period.
Carter Hutton replaced Mazanec in the Nashville goal to start the third period. Mazanec allowed four goals on 13 shots; Hutton stopped all nine shots he faced.
The Predators were 7-1-0 in eight games at home against Carolina under coach Barry Trotz.
"Their top guys were good tonight, and we didn't have a match for them," Trotz said. "Some of our top guys weren't on today. I think our core wasn't as strong. Every moment counts, and those little moments where we forget a play, or we're not ready to play, cost us. They got four goals in 13 shots. That's not a good night for us."
Nashville (13-13-3) was 0-for-4 with the man advantage.
Material from team and national media was used in this report