ORCHARD PARK, N.Y. -- For the first time in a quarter of a century, the Buffalo Bills have won a playoff game.

Playing in front of a home crowd for the first time this season, the Bills beat the Indianapolis Colts 27-24 on Saturday in a wild-card game that was also their first playoff game in Orchard Park since Dec. 30, 1995, when they beat Dan Marino and the Miami Dolphins 37-22.

"It's been a long time since Bills mafia has been able to celebrate like this," quarterback Josh Allen said postgame on CBS. "But again, it's one game. I am just happy for a chance to be able to play next week."

Allen was far improved from his first playoff game last season, completing 26 of 35 passes for 324 yards and two touchdowns, adding 54 yards and another score on the ground. He became the youngest player in NFL history to throw for 300 yards and complete 70% of his passes in a playoff game, per ESPN Stats & Information.

General manager Brandon Beane, who signed a multiyear contract extension in December, said the prospect of bringing a once-proud franchise back to prominence influenced his decision to leave a path to the GM job with the Panthers in 2017 and take over a Bills team that hadn't been to the postseason in 17 years.

Getting a playoff game at home was one of his top priorities once he and head coach Sean McDermott arrived.

"This was an opportunity in a place that's been down for so long that had such a great tradition, and still has a great fan base," Beane said in December. "How exciting would it be to get this thing turned around and host playoff games here? That's what Sean and I want. We want to win the AFC East so that we can host games here. That's been the goal all along, and I think at the end of the day, hopefully, we can get that done this year."

The Bills won the AFC East in 2020 for the first time since that 1995 season, registering their best record (13-3) since 1991 in the process. Riding a six-game win streak entering the playoffs, Buffalo had beaten those six opponents by an average of 19.8 points.

Playing in their first one-score game since Week 8, Allen said Saturday's win proved the Bills can win the close ones, as well.

"This is the playoffs -- this is what it's going to be," Bills receiver Cole Beasley said. "It's going to come down to the wire every time. ... Teams play their best football in the playoffs."

Playing through a knee injury, Beasley caught all seven of his targets for 57 yards. He credited Bills fans -- in the stands for the first time this season -- for a "boost," saying he "needed a little extra" in his first game since Week 16.

Indianapolis took a 10-7 lead midway through the second quarter and nearly extended it when Philip Rivers slightly overthrew Michael Pittman in the end zone on a fourth-down attempt.

Buffalo scored 17 unanswered points following the stop, and the teams traded points in the fourth quarter en route to a thrilling finish.

Trailing by three points with 2:30 remaining in the game, the Colts marched their way downfield and converted on fourth-and-10 on a pass from Rivers to Zach Pascal -- who seemingly fumbled after the catch. Pascal was ruled down by contact, and the call stood after a booth review.

Buffalo knocked down Rivers' Hail Mary attempt with time running out to seal the victory.

Indianapolis had scored on each of its previous two drives, but Bills coach Sean McDermott felt confident in his defense to hold firm one last time.

"Looked like it was well executed by our defense," McDermott said. "I liked the look in their eye when they took the field for that last drive."

Watching the ball sail through the air on the final play brought back memories of the Bills' loss to the Cardinals in Week 10 -- but more so for fans than players. Safety Jordan Poyer said he had "all the confidence in the world" throughout the play, as did Dawkins watching from the sideline.

"This time I was happy that it was going up there. Our guys practice it every single day; I see it every single day in practice," Dawkins said. "I don't want to speak for future days, but they practice for it not to happen. When it went up, I was less stressed because my dogs are prepared for this moment. As you see, Micah [Hyde] went up and tomahawked that ball down like he was a starter on the volleyball court.

"That was a double-hand tomahawk spike as a statement, like it wasn't happening again."

The Bills will host a divisional playoff game next weekend, with their opponent to be determined.

"One's not good enough for us," Allen said. "We've got to find a way to put our best foot forward this week and get another one."