Artemi Panarin had three assists, giving him three straight multipoint games to start the season (two goals, five assists). Reilly Smith scored his first goal for the Rangers (2-0-1), and Alexis Lafreniere and Chris Kreider also scored.
"There's more we definitely could have done, but obviously [Shesterkin] was a really, really big difference in it," Red Wings coach Derek Lalonde said. "He's special."
Lalonde, referring to a report earlier this month that Shesterkin, who can become an unrestricted free agent after this season, turned down an 8-year contract offer at $11 million a year from the Rangers, said, "I can see why he turned down the 88 (million dollar contract). Good agent."
Dylan Larkinscored, and Patrick Kane had an assist for his first point of the season for the Red Wings (1-2-0), who were 0-for-4 on the power play and fell to 1-for-11 through three games. Alex Lyon made 24 saves in his first start for Detroit.
The Red Wings and Rangers play again at Little Caesars Arena on Thursday.
"I thought we had enough looks to win this hockey game and it just didn't go in," Larkin said. "A little bit of credit to Shesterkin. I don't think we sifted enough pucks through traffic and made second and third opportunities, but it's something to learn from and we've got these guys again on Thursday. If he's playing, we've got to remember that he struggles with second and third opportunities. Other than that, if you've got him one-on-one, he's a world-class goalie. We've got to make it hard on him."
Lafreniere gave the Rangers a 1-0 lead at 11:45 of the first period, scoring on a one-timer from the right face-off circle off a pass from Panarin.
"He say he tried bar down, but he went five-hole like usual," Panarin said. "We talked about that play before, like when I go in the middle, he kind of pulls out a little bit for a one-timer. He did that. He hit the net and it go in. Everyone happy."