The Rangers have lost four of their last five since a four-game unbeaten streak, including Wednesday's 2-1 loss to the Montreal Canadiens.
Chris Simon scored for the Rangers, 1-7-2 this season when allowing the first goal.
"I think, as a team we need to play better for sixty minutes," Simon said. "We're working hard, and it just seems that every mistake we make ends up in the net."
The Rangers lost 3-2 to Tampa Bay in their previous game Sunday, dropping them to 0-7 in one-goal games.
"You can't get down," forward Anson Carter said. "It's a long season, and we need to find some goals. Obviously these two games were tough losses for our hockey club, being games against Eastern Conference teams, and we're fighting for that last couple of playoff spots at this point in the season."
New York might be glad to get back on the road. They have lost three straight at home, but are 3-1-1 in their last five games away from Madison Square Garden.
The Sabres are coming off Wednesday's 7-2 loss to the Detroit Red Wings, their third straight defeat and third in four games.
Ryan Miller, recalled from Rochester of the AHL on Monday to fill in for injured backup Mike Noronen, allowed five goals in the final 12 minutes of the third period. Noronen cut his neck during practice Monday.
"I'm disappointed, obviously," said Miller, who made 16 saves.
"I know we are pressing to try and score goals," coach Lindy Ruff said. "The mistakes we are making are huge mistakes. We allowed Detroit to run away with the game."