New York (40-19-5) was coming off back-to-back weekend road wins against the Tampa Bay Lightning and Carolina Hurricanes, and had won four of five games.
"You play those two big games on the road and you win both of those games, and the Carolina game we didn't play well but we won, so it was two big emotional wins," Rangers coach Gerard Gallant said. "You come in here, a team that's not in the playoffs, they're a young team, they're a talented team, a skilled team. They've had trouble winning games. They've had so-called goalie issues, but the kid [Daws] played well tonight and he played well against us the last time we played. And we just weren't mentally sharp from what I saw."
New York goalie Igor Shesterkin made 19 saves but allowed at least four goals for the third time in five starts since March 10 after not giving up more than three goals in 18 straight starts from Dec. 31-March 6. Alexandar Georgiev made five saves in relief in the third period.
But the Rangers didn't blame Shesterkin.
"We had a great first, everyone was in a good mindset, and I think it was just mental errors, some stupid hockey by everyone," forward Ryan Strome said. "Just mistakes that cost us. Weak hockey and soft hockey."
Andrew Copp had two assists in 17:39 in his first game after the Rangers acquired the forward in a trade with the Winnipeg Jets on Monday.
Tyler Motte played 13:06 and had four shots on goal and three hits in his Rangers debut. They got the forward from the Vancouver Canucks on Monday.