Alex Iafallo also scored for Winnipeg.
Adrian Kempke and Mikey Anderson replied for L.A.
Connor Hellebuyck made 29 saves for Winnipeg, while Darcy Kuemper stopped 25 shots for Los Angeles.
Scheifele picked a Josh Morrissey pass out of the air and deflected it past Kuemper to give Winnipeg a 3-2 lead midway through the third period.
Scheifele tied the score 2-2 with 1:03 left in the second. In the tail end of killing a penalty, Morgan Barron stole the puck and fed Scheifele, who raced down the ice and his backhand deflected off Anderson past Kuemper.
The Kings took a 2-1 lead midway through the middle frame. Kempke finished off a pretty three-way passing play with Anze Kopitar and Andrei Kuzmenko at the 9:12 mark.
Anderson knotted the score at 1-1 just 50 seconds into the second period. His screened shot from the point got by Hellebuyck. Drew Doughty and Kempke assisted.
Winnipeg had taken a 1-0 lead into the second period.
Iafallo opened the scoring on the power play early in the first period when he was set up by Kyle Connor alone in front of the net. Gabriel Vilardi also assisted.
Jets: They dominated play in the first period, outshooting L.A. 14-8 and scoring the only goal. After struggling through most of the second, they came back to life in the third.
Kings: After an incredibly slow start, they dominated Winnipeg in the second period, outscoring the Jets 2-1. But they were on the heels in the third, surrendering Winnipegâ€s winning goal.
Scheifele tied the score 2-2 just after killing off a penalty late in the second period to revive the struggling Jets. His backhand got banked in past Kuemper off a defenceman.
Hellebuyck made a number of brilliant saves, especially late, to hold off the Kings.
The Jets will face the Islanders in New York on Monday.
The Kings will play the Wild in Minnesota on Monday.
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