Winnipeg (33-21-12) took the lead at 10:52 of the second period on a goal by Blake Wheeler, and Hutchinson made several key saves to help the Jets hold on for the win.
"We did exactly what we needed to do," Hutchinson said. "We played a solid defensive game. We were able to get a huge two points for us. We've done it all season when we've had injury problems. We lost a lot of defensemen earlier in the year, and we just simplified our game. We might not be able to score five goals missing some key players, but you can win games 2-1, 3-1 like we did tonight."
The Jets, who lead the Los Angeles Kings by three points for the second wild-card spot into the Stanley Cup Playoffs from the Western Conference, played without defenseman Dustin Byfuglien and center Bryan Little after each sustained an injury in a 3-1 loss to the Ottawa Senators on Wednesday.
Nashville (41-19-7) has lost a season-high six consecutive games and four in a row at Bridgestone Arena. The Predators lead the St. Louis Blues by two points for first place in the Central Division.
Goaltender Pekka Rinne lost for the first time in his career against Winnipeg (7-1-0).
"When you struggle, it seems like it's tough to get out of that hole," Rinne said. "You just have to believe it and keep working. Tonight, the effort was there. Right now it seems like the tiniest mistakes we make, the puck seems to end up in our net. It's tough. The margin is so small and so slim. You just have to believe and keep working hard.
"I thought that we played another solid game like the game before, but we're just not getting the results right now and it's tough."
Michael Frolik scored his 15th goal to give the Jets a 1-0 lead at 14:54 of the first period on a one-timer next to the crease that beat Rinne. Forward Andrew Ladd made a move to get around Nashville defenseman Seth Jones and passed it to Frolik.
"That's why [Ladd] is our captain," Wheeler said. "He led the way, got us going tonight, got us off to a good start, and we all followed from there. We all follow in line when he's going like that, and it was a big start for that line."
Nashville defenseman Ryan Ellis tied the game 1-1 at 10:17 of the second period on a wrist shot from the point. Ellis' shot hit a Winnipeg player in front, changed directions and went past Hutchinson for his sixth goal.
"We didn't get as many looks or attempts as we normally get," Predators coach Peter Laviolette said. "When we did get some, we had some good scoring opportunities, and [Hutchinson] played really well tonight. It was difficult."
Wheeler put the Jets back in front 35 seconds after Ellis' had tied it. He scored on a rebound given up by Rinne, who made 23 saves. Defenseman Tyler Myers took the original shot, and the rebound went straight to Wheeler, who shot it in the wide-open net for his 18th goal.
"I thought everyone was doing the little things," Myers said. "The forwards did a great job of reloading high so the defense could be aggressive in the offensive zone, which allowed more zone time for us. Defensively, we did a good job of communicating, not getting two guys jump into one guy. It was just an all-around really good effort for us."
Drew Stafford's empty-net goal with 49.9 seconds remaining made it 3-1. Nashville initially pulled Rinne with 3:12 remaining in regulation, but Winnipeg was able to prevent them from sustaining pressure in the offensive zone.
"Our gap was good," Jets coach Paul Maurice said. "There was no easy ice to play on out there. We blocked shots when we had to. We didn't pull back in our neutral zone, we didn't pull back off our forecheck much. It was a hard game for either team to get pucks to the net."
Predators defenseman Cody Franson left the game with an apparent injury at 15:04 of the second period but returned for the start of the third.
"A little bit like the whole game, he gets a pretty good knock into the crease there," Maurice said. "We had [goaltender Ondrej Pavelec] stretching because I thought with the force of that he was coming out, but he went back in and was just fantastic."