Tanev gave the Jets a 1-0 lead at 14:51 of the first period, scoring on a rebound at the left post off an initial shot by Bryan Little.
Stastny made it 2-0 at 9:01 of the second period. After a scramble in front, Patrik Laine collected the loose puck and shot from the left circle, and Stastny got the rebound and scored into an open net.
"Opportunistic, for sure," Stastny said. "When you get your chances, you've got to score. We didn't get any power plays. Sometimes, when you get power plays, you feel the puck and you get more chances. When you don't, we had different lines kind of step up and make plays.
"But our goals were more simple plays. When we didn't make the simple plays and were trying to do too much, trying to feather on 2-on-1s or 3-on-2s or over passing a little bit, then we got in trouble. If you look at the ways we scored, we just went to the net and from there, created everything."
Scheifele extended the lead to 3-0 at 17:51 on a rush, taking a drop pass from Wheeler and beating Rinne blocker side from the high slot.
Juuse Saros replaced Rinne to start the third period and made two saves.
Fiala scored to cut it to 3-1 at 1:23 of the third period. It was the first goal Hellebuyck had allowed since Marcus Foligno scored for the Minnesota Wild at 18:23 of the second period in Game 3 of the first round (163:00).
Scheifele scored an empty-net goal with 36 seconds remaining to make it 4-1.
"We're an upbeat group in here," Nashville defenseman P.K. Subban said. "If I'm being honest, that's the best game we've played probably of the playoffs and maybe one of our best of the year. The bounces didn't go our way. That's one that we're OK (with). We'll all sleep well tonight and we'll be ready to go back at it on Sunday."