Dustin Byfuglien scored twice in regulation for the Jets (20-21-3), while Bryan Little and Nikolaj Ehlers added goals as well. Rookie Connor Hellebuyck stopped 31 shots for the win, making his ninth start in Winnipeg’s last 10 games.
Ryan Johansen, Eric Nystrom and James Neal all scored in the third period as Nashville (19-18-7) rallied from a 4-1 deficit. Kevin Fiala opened scoring for the Predators in the first period as Pekka Rinne made 19 saves.
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 saw nearly two minutes of 3-on-3 hockey, Neal's equalizer with 13.5 seconds remaining in the third sent Nashville and Winnipeg to another round of 3-on-3 in overtime.
The Jets held a 4-1 lead in the third after rookie Ehlers scored his eighth goal on the year, but Nashville responded with goals less than three minutes apart midway through the period as recent addition Johansen and Nystrom scored to made it 4-3 with 8:07 to play.