Prior to Sunday, Buffalo had the longest active playoff drought in all four major U.S. team sports. They will travel to Jacksonville next weekend.
But the Bills (9-7) suffered a key injury in the third quarter when six-time Pro-Bowl running back LeSean McCoy left the game in the third quarter due to an injury to his right ankle. He did not return.
Meanwhile, Miami (6-10), which has missed the playoffs in 14 of the past 16 years, challenged late with 13 consecutive points and a recovered onside kick with 1:52 remaining. But an interception by safety Jordan Poyer -- his fifth of the season -- sealed Buffalo's win.
Bills quarterback Tyrod Taylor completed 19-of-27 passes for 204 yards and one touchdown with no interceptions. He also scrambled for 35 yards.
Prior to Sunday, Fales had attempted just six NFL passes. He completed 29-of-42 passes for 265 yards with one interception and one touchdown pass against Buffalo. He also scored his first career touchdown.
Cutler's 12-year NFL career, meanwhile, may be over. He retired after last season, but returned when Dolphins quarterback Ryan Tannehill got injured.
Buffalo never trailed.
The Bills scored on their opening possession as Taylor rolled left and threw to the right, hitting a wide open Nick O'Leary in the end zone for a 26-yard touchdown.
O'Leary, a tight end from nearby West Palm Beach, Fla., is the grandson of golfing legend Jack Nicklaus, who was in the stands on Sunday. It was O'Leary's second career touchdown catch.
On Buffalo's next drive, Taylor overthrew an open O'Leary in the end zone, and the Bills settled for a 23-yard field goal by Stephen Hauschka.
After a 51-yard, third-quarter field goal by Hauschka, the Bills increased their lead to 19-0 on a one-yard run by 12th-year defensive tackle Kyle Williams, who scored for the first time in his career.
The game's final minutes featured fireworks.
That ruling was reversed on video review, and Landry scored on the next play on a 1-yard pitch. After scoring, Landry charged toward Poyer, and their helmets crashed.
A melee ensued, and Dolphins running back Kenyan Drake flung a Bills helmet. Landry and Drake were ejected.
With 1:56 left in the fourth quarter, Fales scored on a 1-yard run, closing Miami's deficit to 22-16.
Miami then recovered its fourth onside kick of the season -- most in the NFL -- but that was as close as it got for the Dolphins.
NOTES: Bills CB EJ Gaines (knee) returned after missing one game. ... Bills CB Shareece Wright (concussion) sat out. ... Bills G John Miller (ankle) missed his seventh straight game. ... Dolphins LT Laremy Tunsil (ankle) sat out for the first time this season. Three other opening-day Dolphins starting offensive linemen also finished the year injured: RT Ja'Wuan James (hamstring) and Gs Jermon Bushrod (foot) and Anthony Steen (foot). ... Dolphins C Mike Pouncey, bothered by a chronic hip injury, started all 16 games for the first time since 2012. ... Miami placed WR Leonte Carroo on the non-football injury list after he had an undisclosed medical procedure. ... Miami placed DT Vincent Taylor (knee) on injured reserve.