Joel Eriksson Ek, Mats Zuccarello and Dmitry Kulikov scored, and Kirill Kaprizov had two assists for the Wild (30-12-3), who had won 11 of their previous 13. Cam Talbot made 25 saves.
"We didn't like our game right from the start," Minnesota coach Dean Evason said. "We didn't finish checks. We were going a lot of east-west. Winnipeg did a lot of really good things against us, again."
Scheifele tied it 1-1 at 11:20 of the second period, then gave Winnipeg a 2-1 lead on the power play at 19:48 with a one-timer from the left face-off circle. He extended the lead to it 3-1 at 1:07 of the third period to complete the hat trick.
"They kind of took over a little bit in the second there," Wild defenseman Alex Goligoski said. "We left Cam out to dry. A couple backdoor goals, breakaway, deflection. It's a 60-minute game. We can't take shifts off and stuff like that, and I think that was the story tonight."
Eriksson Ek gave Minnesota a 1-0 lead at 10:29 of the first period.
"We had a good first period, we looked really good," Wild forward Marcus Foligno said. "They keep working there and they're desperate, and that's how they played in that second period. … We've been on a roll and it's been good hockey as of late. We just run into these rivals and sometimes it's tough sledding."
After Scheifele's three goals, Perfetti extended the lead to 4-1 at 2:23 of the third when Nate Schmidt's point shot deflected off of him.
"It's a good feeling," Perfetti said. "A little bit of a lucky one. I guess just go to the net and let it hit you. That one hit my arm. Fortuitous bounce."