Josh Morrissey made it 6-3 at 14:48, scoring into an empty net. It was his seventh goal of the season, tying his NHL career high from 2017-18.
Ross Colton cut it to 6-4 at 17:15 before Stastny scored into an empty net at 17:29 for the 7-4 final.
"No question, we're in a funk right now," Tampa Bay coach Jon Cooper said. "Everybody has just got to dig a little deeper and get yourself out of it. Are the starts concerning? There's no question, but hitting the panic button with this team? Not a chance. You have some tough nights. We just happen to have a few in a row, and it really hasn't shown up in the win-loss column, but we haven't played our best."
Scheifele gave the Jets a 1-0 lead at 4:19 of the first period, scoring with a backhand after Logan Stanley hit the post on a shot from the point.
Adam Lowry made it 2-0 at 6:11, scoring on his own rebound following a tip in front.
"How many times now in a row have we started behind in a game having to claw ourselves back," McDonagh said. "It's not ideal and it's not winning hockey. We need to individually look at ourselves, change it up and do something different to get ourselves mentally engaged, playing with some pace and playing with some determination to start a game, at least not give ourselves a hole to climb out of."