Nikolaj Ehlers scored, and Connor Hellebuyck made 28 saves for the Jets (29-24-5), who had a three-game winning streak end.
"Their guy was pretty good," Winnipeg coach Paul Maurice said. "There were some that we missed on, broke some sticks, didn't get a tip on. There's some of that stuff. But their guy made some pretty good saves in tight. He was positionally, really, really square to pucks. He was good."
Chris Kreider scored twice for the Rangers (28-23-4), who have won five of their past seven games with Shesterkin winning four.
"A rising tide lifts all ships and the team's playing well," Kreider said. "Good chemistry up and down the lineup. Guys are getting more comfortable with each other. Young guys are growing up every single day. It's unbelievable to see how much everyone's progressing, how much everyone's improving, so that's something we've focused on and that's something we've got to continue to focus on."
Kreider scored with 35 seconds remaining in the first period to give the Rangers a 1-0 lead, and at 7:30 of the second period to make it 2-0.
New York scored twice in the opening 1:28 of the third period. Ryan Strome made it 3-0 at 53 seconds, and Mika Zibanejad extended the lead to 4-0 35 seconds later. Ehlers ended the shutout at 4:35, making it 4-1.
"We had a plan before coming out for the third and we weren't able to do that," Ehlers said. "You get two goals against and you keep going. The game isn't over. I think the way we played in the third we worked our (butts) off, we got pucks deep and got some big chances."