The shutout was Shesterkin's fourth of the season and sixth in 89 NHL starts. He allowed six goals on 44 shots in his previous two starts, a 3-0 loss to the New York Islanders on April 1 and a 4-3 shootout loss to the Philadelphia Flyers on April 3.
"I thought he was excellent," New York coach Gerard Gallant said. "People were worried about him. I wasn't. He played really well tonight, made some real key saves at key times."
Artemi Panarin scored in his 500th NHL game, and Frank Vatrano scored his sixth goal in 12 games for the Rangers (46-20-6), who are 6-1-1 in their past eight games. They are second in the Metropolitan Division, two points behind the Carolina Hurricanes and six ahead of the third-place Penguins.
Pittsburgh (41-21-10) is 2-5-1 in its past eight, including losses to New York on March 25 (5-1) and March 29 (3-2). Center Sidney Crosby did not play because of a non-COVID-19 illness, and Tristan Jarry made 21 saves.
"We're competing hard," Penguins coach Mike Sullivan said. "We're in every game. When you look at the last handful of games, I feel like the team's played pretty hard. We haven't got the result, but we just have to continue to stay with it. That's the message that we gave the guys after the game.
"We've got to learn through each experience. We can't dwell on it."