The Sabres’ determination put them in position to win, but it was Mike Smith who carried Buffalo to victory.

The Phoenix Coyotes goaltender made the mistake of flying by the seat of his pants Monday night, a decision that delivered a 2-1 overtime win to the Sabres. Smith and teammate Martin Hanzel reached up to grab an airborne puck, and neither succeeded. Smith had no idea the puck landed in the back of his pants, so he slid into the net to block the goal line.

By doing so, he put the puck in the cage. The referees briefly conferred and awarded Mark Pysyk a game-winning goal.

“I knew the puck went up in the air, but I had no idea where it went after that,” Smith said in First Niagara Center. “I guess if they don’t see the puck they’re supposed to blow the whistle, but that’s not what happened.”

The Sabres gladly accepted the break. They worked to earn one.

For the first time in almost 33 years, Buffalo played two skaters shy of a full roster. They started with just 16, which coach Ted Nolan divided into nine forwards (three regular lines) and seven defensemen. The second-period ejection of right wing Drew Stafford cut the number to 15.

“That was a gutsy win for us, for sure,” Nolan said. “You’ve got to give this team a lot of credit. They had good perseverance. They kept at it.”

The Sabres hadn’t used 16 skaters since Jan. 7, 1981, when they managed to beat the Quebec Nordiques, 5-1. They won again, this time without defenseman Alexander Sulzer and forwards Marcus Foligno, Linus Omark and Ville Leino, who missed the game with flu-like symptoms.

“I’ve never played an NHL game like that, but sometimes you face tough circumstances,” Sabres forward Matt Moulson said. “This team pulled together and battled hard. That was a big emotional win.”

The extra workload up front was felt most by Moulson (23:36 of ice time), Steve Ott (22:02), Zemgus Girgensons (22:01) and Tyler Ennis (21:58). They’re happy the Sabres are starting a three-day holiday break. They could use the rest.