Callahan took a pass from defenseman Ryan McDonagh and broke in alone. He flipped a shot over goalie Ryan Miller's shoulder for his career-best 24th goal of the season. New York was 0-1-1 in its previous two games, its first losing streak since mid-December.
The Rangers got tying goals from Carl Hagelin in the second period, and Marian Gaborik in the third. New York (39-15-6) has an Eastern Conference-leading 84 points — seven more than Boston.
Drew Stafford scored both goals for the Sabres (27-27-8), who are 11th in the East — six points below the postseason cutoff. Buffalo had won three straight. The Sabres, coming off a 3-0-1 homestand, opened a five-game road trip.
Gaborik scored his team-leading 29th goal at 5:32 off a perfect pass from defenseman Michael Del Zotto to tie it 2-2. Playing in his 700th NHL game, Gaborik took the pass on his forehand in the left circle before streaking in on Miller and flicking a backhand over his left shoulder.
Stafford gave the Sabres a 2-1 lead 44 seconds into the third period with a wrist shot over the left shoulder of goalie Henrik Lundqvist during a power play.
Stafford opened the scoring at 15:29 of the first period off a pass from Tyler Ennis, who took advantage of a loose puck in the corner to the left of Lundqvist.
Hagelin tied it at 7:38 of the second, banking the puck off of Miller's pad for the 10th goal of his rookie season.
The Rangers won the first two meetings between the teams in Buffalo: a 1-0 shootout victory on Feb. 1 and a 4-1 win on Dec. 10.
NOTES: The Sabres are 6-3-3 since the All-Star game. . Buffalo has had 22 players miss at least one game because of injury. Only RW Jason Pominville and G Jhonas Enroth have been in the lineup for every game. ... The Rangers have at least one point in 40 of 52 games a 3-3-2 start to the season.