Cody Glass had the other goal for Nashville, winners of four of five.
Pierre-Luc Dubois scored and Connor Hellebuyck made 39 saves for Winnipeg, which concluded a season-long five-game road trip 2-3-0.
At 5:38 of the third, Jeannot picked up the rebound of a Tommy Novak shot and beat Hellebuyck with a wraparound.
The goal not only broke a 1-1 tie, it snapped a 38-game goalless stretch for Jeannot, who scored 24 goals last season.
Dubois scored the game’s first goal 48 seconds into the opening period off of a slick backdoor feed from Cole Perfetti. The goal was the fastest from the start of the game for the Jets this season.
Glass tied it at 13:49 of the second, deflecting a Roman Josi shot from the blue line.
Tuesday was Nashville defenceman Alexandre Carrier’s 141st NHL game, but it took him until then to record his first fighting major. Just over a minute into the first, Carrier took exception to a hit Jets defenceman Logan Stanley put on Glass along the left boards.
At 5-foot-11 and 174 pounds, Carrier is much smaller than the 6-foot-7, 228-pound Stanley.
After serving his penalty, Carrier played five more shifts in the first period, but he did not return to the bench for the start of the second period or play in the remainder of the game. The Predators did not provide an update on his condition during the game.
STRONG CENTRAL RECORD
Despite Tuesday’s loss, the Jets still sport a strong 12-4-0 record against fellow Central Division opponents. Winnipeg and Nashville have split the two games they have played against each other so far this season, with each winning on home ice. The two teams will play twice more this season, once in each city.
Predators: Host the New Jersey Devils on Thursday.
Jets: Host the Buffalo Sabres on Thursday.