"I think I've felt good so far this whole preseason, season," Hutton said. "You get some breaks and we battle hard. I thought I fought hard through traffic to find pucks, and we did a good job of eliminating second chances. And I think the special teams tonight is the difference."
Conor Sheary scored his first two goals for the Sabres, who lost their season opener 4-0 to the Boston Bruins on Thursday.
WATCH: [All Rangers vs. Sabres highlights]
New York lost its second straight, including 3-2 to the Nashville Predators on Thursday.
"We did a lot of good things better than we did the other night," Rangers coach David Quinn said. "At the end of the day, though, this is a game of taking advantage of your opportunities, and they took advantage of two of theirs and we only took advantage of one of ours."
Sheary scored Buffalo's first goal of the season on the power play at 13:15 of the first period for a 1-0 lead. Rasmus Ristolainen sent a cross-ice pass to the left wing on a 2-on-1, and Sheary beat Henrik Lundqvist stick side from the left circle.
"It's been a while since I scored going back to last year, so that one definitely felt good," said Sheary, who was acquired this offseason in a trade with the Pittsburgh Penguins. "To get your first one on a new team as well I feel is important and kind of let me relax the rest of the game."