Hutton was making his ninth start of the season and first since Jan. 27 in place of No. 1 goalie Pekka Rinne with Nashville playing the second game of a back-to-back. It was his second shutout this season and the fourth of his NHL career.
"Whenever they give me starts, I play," Hutton said. "Anything I can do to help our team win. I understand my role. At the same time, just any way I can contribute is what I try to do."
James Neal had a goal and an assist, and Miikka Salomaki and Shea Weber scored for Nashville (26-21-9), which had lost four of five, including 4-3 in overtime against the Tampa Bay Lightning on Friday. Mike Ribeiro and Roman Josi each had two assists.
Video: NSH@FLA: Jarnkrok beats Luongo, Preds take early lead
Nashville was 2-for-3 on the power play after going 2-for-20 in the previous five games. Florida was 0-for-4 and has failed on all 13 opportunities in its past four games.
"I thought we controlled it pretty good once we got it in there," Predators coach Peter Laviolette said of their power play. "Right now, [the Panthers have] given up a few goals and we talked about that, trying to exploit it. But they've got good penalty-killers over there. Right now, they might be in a little bit of a rut, so we were able to take advantage of it."
Jarnkrok's second goal of the night and 11th of the season made it 5-0 at 13:48 of the third period. It was Nashville's sixth goal while shorthanded and Jarnkrok's fourth in the past five games.
Roberto Luongo, in his second start in two nights, made 23 saves for Florida. He was pulled following the first period Friday after allowing three goals on 13 shots in a 5-3 loss to the St. Louis Blues, and has allowed at least three goals in each of his past five starts.
Video: NSH@FLA: Jarnkrok scores his second goal shorthanded
Panthers coach Gerard Gallant disagreed with the notion that Luongo is struggling.
"No, our team is," Gallant said. "He hasn't been as sharp as he was, but it's our team the last couple of games."
The Panthers (32-18-6) have lost four of five following a 17-3-1 stretch. They were shut out for the fourth time this season and second time in four games. The loss Saturday was their first at home by more than two goals.
Florida was 11-1-1 in its previous 13 home games before the back-to-back losses against St. Louis and Nashville.
The second period was stopped with 32.1 seconds left after a puck sent over the glass by Hutton struck a young girl in the face. Hutton gave the girl his goalie stick before she left the arena under her own power.
"Obviously, you feel bad," Hutton said. "It [stinks]. At first, I didn't even realize. All I'm trying to do is make sure I get glass on it so it's not a penalty, and it hits a little kid. I didn't really see if it was a boy or a girl; someone just said it hit a little kid. So I just tried to get a stick over to give to the little kid. I'm sure at that point, they probably wanted to break the stick. It was the least I could do. Obviously, I felt pretty bad. It was one of those things, unfortunately."
Florida forward Quinton Howden left the game in the second period with an upper-body injury after Nashville defenseman Anthony Bitetto's shoulder hit his face on a body check in the neutral zone. Bitetto was not penalized on the play.
Video: NSH@FLA: Neal increases the Predators' lead
Panthers forward Brandon Pirri left with an apparent left-ankle injury with 2:21 left in the third period after crashing into the boards fighting for position with Predators defenseman Ryan Ellis.
The Florida bench was assessed a bench minor for abuse of officials after that play, and Gallant was assessed a game misconduct.
Nashville led 2-0 after its first multigoal first period in 22 games.
Jarnkrok opened the scoring at 6:18 when he took a feed from Neal, skated in from the right wing and beat Luongo with a shot to the glove side from in tight.
Salomaki made it 2-0 at 8:24 after Austin Watson won a battle along the boards and fed him in the right circle. Salomaki skated to the left of the faceoff dot before beating Luongo high to the glove side with a wrist shot.
Video: NSH@FLA: Salomaki increases the Predators' lead
"You do play a little bit of a different game (with a lead)," Laviolette said. "It hasn't happened a lot lately. We've been in a position where we're always coming from behind or we give up a couple goals or whatever it might be, so it was nice to get the lead and play on top. It's a different mindset."
Neal made it a three-goal lead at 10:24 of the second period with a power-play goal. Ryan Johansen's deflection of a hard Ribeiro pass squeaked past Luongo and was sliding toward the net before Neal came in from the side and made sure.
The goal came with Panthers forward Reilly Smith in the penalty box for high sticking, a penalty that occurred on the faceoff after Howden was injured.
Hutton, who made 29 saves in a 3-0 victory against the Minnesota Wild on Jan. 16, made a spectacular save later in the second period when he slid across the crease to stop Jonathan Huberdeau's redirect on a 2-on-1.
"I kind of read the pass and just tried to extend as far as I could and was able to get my blocker on it. Obviously, at that point in the game, sometimes it's not as many as you make, it's kind of the timely ones. And we were to roll from there and get a couple of big power-play goals that kind of put the nail in the coffin."
Weber made it 4-0 at 7:59 of the third period after Florida defenseman Brian Campbell was called for playing with a broken stick. Weber scored on a one-timer from the left dot.
Video: NSH@FLA: Weber scores on power play with slap shot
After going 1-0-1 on its fathers' trip, Nashville will be home for its next game, Monday against the Dallas Stars.
"It was a big win for us with a real tough loss yesterday against Tampa Bay," Jarnkrok said. "We wanted to end the road trip the right way."
Panthers forward John McFarland, a second-round pick (No. 33) in the 2010 NHL Draft, made his NHL debut. He became the last of Florida's six picks in the first two rounds of the 2010 draft to reach the NHL, following first-round selections Erik Gudbranson, Nick Bjugstad and Howden, and second-round choices Alex Petrovic and Connor Brickley.
The Panthers again played without injured center Aleksander Barkov and defensemen Erik Gudbranson and Willie Mitchell.
Florida continues its six-game homestand Monday against the Pittsburgh Penguins.
"It's a tough spot," Gallant said. "Men get through it and you battle back. It's two losses in a row where we were no good at all. We're going to play a real good (Pittsburgh) team. You go through tough times and tough injuries, but you play the games. Let's work hard with the guys we've got and go play hard. We're missing some depth, but when nobody plays well, it hurts your team."
Video: Predators shutout Panthers