Will Cuylle had a goal and an assist, Artemi Panarin had an assist to extend his home point streak to eight games, and Igor Shesterkin made 27 saves for the Rangers (9-4-1).
However, four of Winnipeg's goals came off Rangers turnovers, including three by Mika Zibanejad.
"There's isolated incidents for everybody where we could have done something different, whether it be puck decisions or whether it be a little bit more responsible when we're pressing in the offensive zone," Rangers coach Peter Laviolette said. "There are definitely situations that we could have done things better offensively. I still think we were on the attack. It's one of those games where you're punching, trying to punch away at them and generate offense and sometimes you've got to cover up and make sure you're not coming back and leaving it the other way. Those incidents, they cost us the game."
Scheifele gave the Jets a 1-0 lead 57 seconds into the first period, scoring from between the circles off a defensive zone turnover by Zibanejad. Josh Morrissey got the puck on the right-wing wall and found Scheifele in front.
"We hunted it, 'J-Mo' jumped in and kept that puck alive," Arniel said. "This league is about pressure. When you're good at it, you can make it hard on the opposition."
Cuylle made it 1-1 at 13:07 by scoring off a rebound of Braden Schneider's point shot.
Gabriel Vilardi's power-play goal at 8:58 of the second period gave the Jets a 2-1 lead.
K'Andre Miller fumbled the puck behind the net, allowing Winnipeg to sustain possession. Pionk sent the puck to the net and Vilardi tipped it down, slipped around Miller, dished to Ehlers on the right side, and got it back for a tap-in power-play goal.
"Some pretty high-end skill there and finish," Connor said. "You rewind 20 seconds before that, you see that type of end but at the same time we're hunting pucks, we're getting stick on puck on their defender. That's always first and foremost on our power play, stay on the puck, try to turn it over, win those battles, get the puck back and make plays like that."