Cody Glass had the other goal for Nashville, winners of four of five.
''It's nice to see what our group looks like when we are playing the right way,'' Nashville coach John Hynes said. ''We're in a position where we're continuing to fight for wins and move up in the standings, and I think if we continue to build on what we've built the last two games, we give ourselves a really good chance on Thursday.''
Pierre-Luc Dubois scored and Connor Hellebuyck made 39 saves for Winnipeg, which concluded a five-game road trip 2-3-0.
''It certainly wasn't a 2-1 game in terms of offensive opportunities for either team, but both goalies were outstanding,'' Winnipeg coach Rick Bowness said.
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.
''It feels really good, a little bit of a weight lifted off the shoulders,'' Jeannot said. ''My focus has been the same going into every game, just do everything I can to help the team win.''
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.
''(Perfetti) is a great player,'' Dubois said. ''He's smart. He's skilled, he can pass, he can shoot.''
Glass tied it at 13:49 of the second, deflecting a Roman Josi shot from the blue line.
''For me, I just need to bear down on those opportunities and put them in the back of the net because it's not very often you get those chances,'' Glass said.
Tuesday was Nashville defenseman 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 defenseman 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.
''I owe him a dinner or new shoes or something, but that's just the kind of character (Carrier) is,'' Glass said. ''He's a great dude. To fight someone that much bigger than him and have my back is something I'll never forget.''
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. Following the game, Hynes said that Carrier's injury was a result of the fight and that an update on his condition would be provided later in the week.
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.
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