The Predators, who won the Presidents' Trophy, will have home-ice advantage.
It is the third straight season Nashville advanced to the second round; it lost to the Pittsburgh Penguins in six games in the Stanley Cup Final last season and to the San Jose Sharks in seven games in the second round in 2016.
The Winnipeg/Atlanta Thrashers franchise had never won a playoff series.
"It's been a long journey, a lot of ups and downs, not many playoff games," Jets center Bryan Little said. "A lot of long summers watching this hockey, so it definitely feels nice to be moving on and doing well in the playoffs. Once you get that action, that taste, you want to keep going. We're celebrating for an hour in here, then we're getting ready for Nashville ..."
The Predators went 3-1-1 against the Jets during the regular season.
Roman Josi had nine points (one goal, eight assists), Viktor Arvidsson had seven points (two goals, five assists), and Kevin Fiala and Kyle Turris each had three goals and three assists for Nashville. Pekka Rinne, a Vezina Trophy finalist, was 3-1-0 with a 3.52 goals-against average and .901 save percentage, and backup Juuse Saros allowed four goals on 47 shots in his only start, a 5-4 shootout loss March 25.