Hutton had six saves in the first period, 10 in the second and 21 in the third when the Rangers tried to rally from a 3-0 deficit.
Mika Zibanejad and Chris Kreider scored for the Rangers, and Alexandar Georgiev finished with 25 saves.
The Rangers, who speak collectively of putting together a playoff charge to avoid missing the postseason for a third straight season, are 5-5-0 in their last 10 games and sit nine points behind Carolina for the second wild card in the Eastern Conference with the trade deadline looming on Feb. 24.
Rangers coach David Quinn was perplexed by his team’s subpar effort, two nights after they defeated Toronto at home.
“They wanted it more than we did,” Quinn said. ”This was nowhere near what need … nowhere near enough. I am surprised about tonight.”
Vesey, a highly touted free agent out of Harvard who played three seasons for the Rangers before his trade to the Sabres last July, pushed Buffalo’s lead to 3-0 with 8:04 left in the third for his eighth.
Zibanejad ruined Hutton’s shutout bid with his 22nd goal with 2:53 remaining. Artemi Panarin and Marc Staal had assists on the play.
“I don’t know if we matched their intensity,” Zibanejad said. ”It’s all on us. We didn’t put ourselves in a good spot to win the game. We were out of sync. This wasn’t good enough today.”
Kreider then pulled the Rangers within one with his 20th of the season on the power play with 1:38 left. Kreider has goals in eight of the past 11 games. Zibanejad and rookie Kappo Kakko added assists on Kreider’s goal, the fifth time the potential free agent left wing has reached the 20-goal mark.
That was as close as the Rangers got.
The inconsistent Rangers were coming off a 5-3 win over the Maple Leafs at the Garden on Wednesday, two nights after they were smothered at home by the Dallas Stars by the same 5-3 margin.
“They did a good job,” Quinn said of the Sabres, who had lost at home, 4-3 in a shootout to the league-worst Detroit Red Wings, on Thursday. “They were disciplined. Give them credit.”
Georgiev was making his first start since Jan. 21, a 4-2 loss at home to the Islanders. The Rangers have been carrying three goaltenders on their roster since Igor Shesterkin was recalled from Hartford to make his debut on Jan. 7 against Colorado. Shesterkin is 4-1 since his ascension while Henrik Lundqvist has dressed as a backup to Georgiev or Shesterkin on most nights over the past month.
Georgiev had won two of his last three starts – both against the Islanders. He fell to 12-11-1 on the season. Lundqvist has a 10-11-3 mark.
The Sabres had lost three straight against the Rangers while being outscored 15-5. New York had won seven of the last 10 meetings at home.
“It was an unbelievably strong defensive performance by the guys. That was the centerpiece of the victory tonight,” Sabres coach Ralph Krueger said. ”We like our road game. Let’s take it home.”
Girgensons opened the scoring with 9:34 left in the first, getting his 10th goal of the season on a nifty move to beat Georgiev. Girgensons fooled the goalie as he skated into the crease, eventually sliding the puck into the net to Georgiev’s right.
“He has been a solid performer for us,” Krueger said of Girgensons. “We need to get more guys there.”
Reinhart made it 2-0 with 4:44 left in the second, scoring his 20th on a breakaway. Sabres captain Jack Eichel and Vesey drew assists as Reinhart backhanded the puck over Georgiev’s left shoulder. It is the fourth time in five seasons Reinhart has reached the 20-goal mark for the Sabres, who drafted him with the second overall pick in 2014.
“I liked the way we played. They have some world class players,” Reinhart said. ”We held it together.”
NOTES: The Rangers scratched F Micheal Haley, D Brendan Smith and G Shesterkin. … The Sabres scratched D Zach Bogosian and C Rasmus Asplund. … Buffalo also continued to be without injured forwards Kyle Okposo, Victor Olofsson, Vladimir Sobotka and G Linus Ullmark. … The Rangers won the previous meeting 6-2 at the Garden on Oct. 24. … The teams meet again March 22 in Buffalo. … Sabres D Rasmus Dahlin returned after two-game absence with an upper-body injury.