WATCH: All Predators vs. Jets highlights
The Predators had 20 shots on goal in the third period.
Drew Stafford, Mark Scheifele and Adam Lowry scored for the Jets (10-12-2).
Hellebuyck made his 11th start in the past 13 games for Winnipeg and got his second shutout of the season. He made 27 saves in a 4-0 win against the Chicago Blackhawks on Nov. 15.
Juuse Saros allowed one goal on 22 shots in his second start of the season for Nashville (10-8-3). The Predators are 2-7-2 on the road.
"I think we played well the first 20 minutes and then second period wasn't nearly good enough," Predators defenseman P.K. Subban said. "The third period we had opportunities to score but couldn't put it in. We've got to understand that to win on the road, we need to play a full 60-minute game. That's what it's going to take."
Stafford scored his first goal of the season at 15:21 of the second period to make it 1-0.
Stafford played in his ninth game this season and third since returning from a 15-game absence because of an upper-body injury.
"I've really only played three games this year so to get back in and feel like myself again and to be able to contribute on the score sheet was huge," Stafford said. "We needed this tonight."
Stafford nearly scored a few minutes later. Blake Wheeler found Stafford in the slot, but Saros got his glove on the puck to keep it 1-0.
Roman Josi had Nashville's best chance to score on a partial breakaway in the first period, but his deke attempt was saved by Hellebuyck's right pad.
Scheifele and Lowry scored into an empty net in the third period.
Jets forward Nic Petan left the game in the third period because of a lower-body injury and Jets coach Paul Maurice said after the game that he is day to day.
