The 26-year-old Callahan scored his 100th NHL goal 2:59 into the extra session, and New York snapped a rare losing streak with a 3-2 victory over Buffalo on Saturday night.
"That puck will go to my parents for sure, and I know my grandma is very happy tonight," said Callahan, a native of Rochester, N.Y., which is about 75 miles east of Buffalo. "We stayed even-keeled and kept our emotions about us. I thought it was a real solid 60-minute game out of us."
New York was 0-1-1 in its previous two games, its first losing streak since mid-December. The team hadn't lost three straight since the season's first trio of games -- including the opening two in Europe.
Rangers coach John Tortorella has relentlessly preached tight defense and opportunistic offense as the Rangers continue to dominate the Eastern Conference. Tortorella appreciated his team's spontaneous joy after Callahan's winner.
The Rangers bounced back from a tough 4-3 shootout loss at the New York Islanders on Friday night.
"We didn't get frustrated, and stayed with it," Tortorella said. "This was a big win for us. And I loved the celebration. So good for him."
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 the Boston Bruins.
"We wanted this badly. We've been a little bit all over the map the past two weeks," said center Brad Richards, who assisted on Hagelin's goal. "We were trusting and patient that we'd find a way to win it, and we did."
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.
"We worked hard and we battled for a point," Stafford said. "We just have to keep our focus and doing our best. It's an uphill climb."
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.
"We could have won the game," Sabres coach Lindy Ruff said. "We need those extra points."
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.
"They played well. They are a good and fast team," Miller said.
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. Callahan, with his family in attendance, scored the winner in both games.
"Sure, I'm happy. It's something to look back at the end of the year -- to have a career high in goals and your 100th goal," Callahan said. "It's nice to enjoy tonight but come Monday, it's another game."
On Monday, the Rangers will host the New Jersey Devils -- who trail them by 10 points in the Atlantic Division.
The Rangers traded exiled forward Wojtek Wolski to the Florida Panthers for minor league defenseman Mike Vernace and a third-round pick in the 2013 draft. The NHL trade deadline is Monday. ... 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 after a 3-3-2 start to the season . The Rangers improved to 8-1 in games in which Brandon Prust has a fight in the opening two minutes. Prust fought Paul Gaustad just 8 seconds in.