Shesterkin did not allow a goal on the last 25 shots, including 19 after the Rangers took a 2-1 lead. He is 7-1-1 in his past nine starts and has allowed two or fewer goals in eight of them.
"He's been unbelievable," Rangers coach Gerard Gallant said. "I mean, seriously, how many Grade A chances did they get? The rush chances they got, the Grade A chances, the breakaways, he's unbelievable."
Mika Zibanejad and Chris Kreider scored for New York (35-15-5), which is 7-2-1 in its past 10 games.
"I feel like we've been at times playing … like we've been talking about all year," Zibanejad said. "There are moments in the game when they get some momentum and we probably have to do a little bit of a better job to eliminate that time, their momentum swings. Overall, I think we've been doing what we need to do to get the wins."