The Jets started the game a point ahead of Nashville, as both teams look for a way to get into playoff contention.
Winnipeg is now 7-2-0 versus their own conference since Dec. 27. This was only the Jets' second loss in eight games that included wins over NHL-leader Anaheim and Chicago.
Jones got things started with a perfect wraparound at 3:48 that slipped by Ondrej Pavelec but Thorburn tipped in his first goal of the season off the faceoff for the Jets just 22 seconds later.
Winnipeg struggled at times to get the puck out of their own zone in the second period.
They had a couple of legitimate scoring chances but the closest they came was a post on a long hard shot from Zach Bogosian.
Instead, it was Spaling who snapped one in at 17:18 to put Nashville up 3-1.
But the Jets made up for their early period struggles with two goals in just 27 seconds.
The first was Scheiflele's shot into the crowd in front of Nashville goalie Carter Hutton that bounced in off his one of his own defencemen and it was capped with Wheeler's career-high 22nd of the season at the 18:40 mark.
The Predators had a power-play goal a few seconds into the third waved off for goaltender interference but then Fisher managed one for real at the 42-second mark to make it 4-3.
Notes: Forward Evander Kane was out of the Jets lineup again Tuesday with an infection in the hand he injured a fight with Tampa Bay's Eric Brewer on Jan. 7. Kane initially missed four games but returned Jan. 21 to score a goal and three assists in the next four games. Now he isn't expected to return until after the Olympic break. ... For the pre-game skate the Jets all wore No. 11 jerseys to mark Bell Let's Talk Day and honour Rick Rypien, who signed with the team in 2011 but committed suicide at the age of 27 before reporting and wearing the number he had been assigned. He had a long history of clinical depression.