Scheifele scored on a power play at 8:44 of the first period on a quick one-timer off a cross-crease pass by Iafallo to give Winnipeg a 1-0 lead.
Neal Pionk's first goal of the season at 16:15, a wrist shot from the right circle, made it 2-0.
Pionk got emotional on the bench after scoring; the defenseman attended the memorial service for Adam Johnson, the Nottingham Panthers forward who died Oct. 28 after what the team called a "freak accident" during an EIHL game when he collided with another player and suffered a cut to the neck from the player's skate. Pionk and Johnson were close friends and roommates at the University of Minnesota-Duluth.
“It was big,” Jets associate coach Scott Arniel said. "I know it hit him on the bench there after he did it. I think everybody I know felt it a little bit. It’s been a really tough week-and-a-half, two weeks for him. The thing is, he’s played great hockey for us. It’s probably been a little bit of a release for him to get on the ice and just play and kind of maybe not think about those things."
Thomas responded 40 seconds after Pionk’s goal at 16:55 with a wrist shot from the left circle to cut it to 2-1.
The Blues lamented a number of missed opportunities in the period when Jets defenseman Dylan DeMelo blocked a Pavel Buchnevich shot near the goal line, and Buchnevich had a puck roll off his stick on a breakaway near the end of the period.
Buchnevich has one goal in nine games.
"I'm just awful. I'm just awful all season," Buchnevich said. "I don't know what to say. Guys create chances for me, but I can't finish. I don't know. Hopefully one [will] go in. I just have to play better and help the team. Now I don't create anything, doesn't really help the team. Got to find a way."