MIAMI GARDENS, Fla. -- Finally, the Buffalo Bills can party like it's 1999.

The Bills reached the playoffs for the first time since 1999, defeating the Miami Dolphins 22-16 on Sunday at Hard Rock Stadium.

Buffalo (9-7) had to wait about 15 minutes after its game to officially make the playoffs. That happened when the Baltimore Ravens lost the lead with 44 seconds left and fell to the Cincinnati Bengals, 31-27.

"This is such an emotional moment," Bills head coach Sean McDermott said. "No one gave this team a chance all year long.

"Our fans have been great all season long, and I'm looking forward to seeing them at our playoff game."

Prior to Sunday, Buffalo had the longest active playoff drought in all four major U.S. team sports. Major League Baseball's Seattle Mariners now have the longest drought, dating to 2001.

But despite the joy expressed by McDermott and his players, there was one concern for the Bills, who suffered a key injury in the third quarter when six-time Pro-Bowl running back LeSean McCoy left the game due to a right ankle sprain. He did not return.

Bills quarterback Tyrod Taylor took up the slack, completing 19-of-27 passes for 204 yards and one touchdown, with no interceptions. He also scrambled for 35 yards.

Taylor was thrilled with the Bills making the playoffs, which will begin for Buffalo at the Jacksonville Jaguars next Sunday.

"I watched the end of the Bengals game next to (McCoy)," Taylor said. "I can't even think of the words to describe what our locker room was like.

"The best part is that this is just the beginning."

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 Bills safety Jordan Poyer -- his fifth of the season -- sealed Buffalo's win.

The Dolphins benched veteran quarterback Jay Cutler after just one series, opting for David Fales, a sixth-round pick of the Chicago Bears in 2014.

"I talked to Jay about it," Dolphins head coach Adam Gase said of the decision to insert Fales. "Jay was great. He said, 'Let him play a full game,'"

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.

"I really wasn't too nervous," Fales said. "But running on the field, (the nerves did get) going a bit."

Cutler's 12-year NFL career, meanwhile, may be over. He retired after last season, but returned when Dolphins quarterback Ryan Tannehill got injured.

As for the game details, Buffalo never trailed.

The Bills scored on their opening possession as Taylor rolled left and threw to the right, hitting 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.

Miami's Jarvis Landry broke his own team record with his 111th reception of the season. He fumbled on the play, and linebacker Preston Brown returned the football for an apparent 99-yard touchdown.

But a video review showed Landry had stepped out of bounds before the fumble. Landry scored on the next play -- a 1-yard reception -- for his NFL-leading 112th catch.

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.

The Dolphins kept coming, though.

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.