Ryan McDonagh found Callahan with a pass and the Rangers' captain kicked it from his skate onto his stick blade, eluded a Buffalo defender and fired it past Ryan Miller for the game-winner -- his 100th career goal.
Carl Hagelin added a goal and an assist, and Marian Gaborik had a goal for the Eastern Conference-leading Rangers, who won for only the second time in five games.
Henrik Lundqvist stopped 18 shots to earn the win for New York.
Drew Stafford scored twice and Miller allowed three goals on 28 shots for the Sabres.
Notable deaths of 2014 [PHOTOS]