Benson made it 2-0 at 8:58 when Rasmus Dahlin's shot from the right point ricocheted off him and into the net.
The Rangers comeback started when Lafreniere scored his first goal on the power play at 19:21 to cut the Sabres' lead to 2-1.
He scored again at 2:57 of the second period, beating Luukkonen on a breakaway to make it 2-2.
Fox scored a power-play goal with a point shot through Lafreniere's netfront screen to give New York a 3-2 lead at 14:44 of the second.
The Rangers killed a pair of overlapping penalties, including 56 seconds of a 5-on-3 power play for the Sabres, to maintain the one-goal lead going into the third.
But Tuch evened it at 3-3 at 5:51 of the third period with a deflection of Peyton Krebs’ shot from the point.
"It's a sifter from the blue line," Sullivan said. "We got an opportunity to get in the shot lane. We don't. Then we don't get the stick at the netfront. Those are hard plays to defend. The best way to do it is if we can deny the shot. Then you don't have to defend the netfront."
Zucker gave Buffalo a 4-3 lead at 7:14 by collecting a rebound of McLeod's shot from the left point and tucking the puck around Shesterkin's outstretched left pad.
"I'm just trying to get it to the far side, make him move and see if something opens up," Zucker said. "At that point I realized I had a little bit more time. They lost coverage so I was lucky enough to get it around his pad and stuff it in."
Benson capped it with an empty-net goal at 18:45 for the 5-3 final.
"Huge," McLeod said. "We know the race that we're in and what we're playing for. Not our best, but we got the two points and that's all that matters now."
NOTES: The Sabres earned their 20th comeback win of the season, marking the second time in the past 15 years that they have recorded at least that many in a season. They had 22 in 2022-23, when they missed the playoffs by one point. … Fox extended his point streak to eight games (15 points; four goals, 11 assists).