Dustin Byfuglien scored twice in regulation and Bryan Little and Nikolaj Ehlers added goals for Winnipeg. Rookie Connor Hellebuyck stopped 31 shots.
Ryan Johansen cut Nashville's deficit to 4-2 with 10:59 remaining, Eric Nystrom scored less than 3 minutes later and then James Neal tied it with 13.5 seconds left. Kevin Fiala scored in the first period and Pekka Rinne made 19 saves for the Predators.
Byfuglien left the game in the third period with an undisclosed injury.
Entering Thursday night, Rinne was 1-8-2 with a 3.29 goals-against average in his last 11 road starts.
Following a feverish finish to regulation that included nearly 2 minutes of 3-on-3 hockey, Neal's equalizer sent Nashville and Winnipeg to more 3-on-3 in overtime.
Byfuglien bookended three second-period Winnipeg goals. The Jets put an end to their three-game slide, closing the gap between the two division rivals.
Nashville has lost five straight and ended its four-game trip without a point.
Byfuglien's 10th and 11th of the season were the first goals for the Jets' lone All-Star selection since Dec. 18.
The Predators opened the scoring just 59 seconds after puck drop. A video review placed roughly 10 seconds back on the score clock when it was determined Fiala's initial shot crossed the line before quickly bouncing off the internal crossbar and out. It was the first NHL goal for the 19-year-old Fiala, playing in his first game of the season and third of his career since being selected 11th-overall in 2014.
Moments after Mark Stuart and Paul Gaustad went off for fighting, Byfuglien found the equalizer for Winnipeg. Following a wrister from the top of the circle, Byfuglien grabbed his own rebound and beat Rinne low stick side 6:32 into the second.
The Jets and their 28th-ranked power play were given ample opportunities against the Predators, seeing five chances with the man-advantage. With Neal off for interference just 1:28 after Byfuglien's equalizer, Winnipeg's leading point-getter Wheeler walked into the slot before quickly dishing off to Little. His one-timer re-established his sole possession for the team lead in goals with his 15th.
NOTES: The Jets play at the Minnesota Wild on Friday night. ... The Predators next game is at home against the Wild on Saturday night.