With 6:50 left, the Rangers hit the crossbar and then Tony DeAngelo capitalized 10 seconds later to make it 4-1.
"They were moving the puck pretty well, especially in the last half of the game," Marcus Johansson said. "They started getting confidence and we've got to fall back to what we've been talking about and not chasing it. We went out of position and they played better than us tonight and that's just the way it is."
Vladimir Sobotka had a low shot go past Lundqvist with 48.9 seconds remaining in the second to put Buffalo back within two. The Sabres had a good push toward the end of the period, but couldn't muster any more offense.
New York scored another pair of goals in the third period to close out the scoring. Lundqvist finished the game with 31 saves.
From the players' standpoint, they're already looking ahead to Friday night's game in Detroit.
"We just have to move on. Truthfully, it's just one loss, whether we lost 10-1 or 2-1. It doesn't matter. It's just one loss," Hutton said. "We have a lot of experience and maturity in this room and Ralph as a head coach is going to keep the boys focused."