The win was their second straight to start the NHL regular season after they gave the Edmonton Oilers a 6-0 drubbing Wednesday night.
Scheifele worked a give-and-go along the faceoff circle with Kyle Connor and chipped the return feed past Soderblom to give the Jets the win.
In fact, Scheifele did all the scoring for a discombobulated Winnipeg squad when he counted the tying goal with 1:04 left in regulation.
Connor Hellebuyck made 25 saves for Winnipeg, who moved to 2-0-0 on the season.
Ryan Donato scored the Blackhawks, who lost their second straight game to start the season.
Arvid Soderblom turned aside 33 shots for Chicago. There was no scoring in the first period.
Ryan Donato scored 16:52 into the second when he skated into a puck at the Winnipeg blue line before moving in and wiring a wrister past Hellebuyck, beating him short side.
The goal was his first of the season.
Mark Scheifele tied the contest at 18:56 of the third period when he dove to get to a rebound off a Nikolaj Ehlers shot before sliding a backhand past Soderblom to send the game into overtime.
Chicago travels to Edmonton Saturday while Winnipeg hosts Minnesota on Sunday.
SHOTS-CHICAGO 26 WINNIPEG 35
ATTENDANCE-14,564
