Netminder Nik Antropov made 37 saves on 40 shots for the Rangers, who have 84 points and occupy the seventh spot in the Eastern Conference playoff chase.
Patrick Lalime yielded four goals on 19 shots before backup goalie Mikael Tellqvist played the third period and stopped the 11 shots he saw.
The fading Sabres have lost four in a row and six of seven. They have an outside chance at a playoff spot, but are in 10th place in the Eastern Conference with 76 points and, with 10 games to play, are five points out of eighth place.
Swim Week Miami Beach 2014 [PHOTOS]