Foligno made it 1-0 1:12 into the game with a one-timer off a backhand pass from Joel Eriksson Ek.
Scheifele scored a power-play goal 39 seconds into the second period on a one-timer from the left face-off circle to tie it 1-1. He has 24 points (11 goals, 13 assists) in his past 15 games.
Wheeler scored a power-play goal 52 seconds into the third period to make it 2-1.
"The power play was really good, and the first two periods were pretty good," Wheeler said. "The third period, obviously after we went up by a goal, they pushed really hard, and we just didn't do a good enough job of tilting the ice back in their direction -- getting some pucks in deep, generating a forecheck, kind of stopping that momentum.
"There were too many plays that [were] put it out of the zone and then change and [the Wild] were able to come back into the zone."
Devan Dubnyk made 19 saves for Minnesota.
"We didn't give up a shot [in overtime], so that's a good start because I'm 1-2 with a 0.0 save percentage so far this year in overtime," Dubnyk said. "So maybe that's our strategy now. It's a good one, though. … We talked about it this past week that we're going to need to get some points in the extra session whether it's overtime or the shootout as we go forward here."