Buffalo can party like its 1999.

MIAMI GARDENS, Fla. — Amid the dancing and screaming and hugs and high-fives in the Buffalo Bills’ locker room, defensive tackle Kyle Williams watched his two young sons climbing around in his stall.

“What do you think, boys?” Williams shouted. “Where are we going? The playoffs?! Yeah!!”

His sons are only 6 and 4. For their dad and most Buffalo fans, Sunday was a long time coming.

The Bills snapped the longest current non-playoff drought in North American pro sports, making the postseason for the first time since 1999. They avoided elimination by beating Miami 22-16, and clinched an AFC wild-card berth minutes later when Cincinnati rallied past Baltimore.

The Bills watched the dramatic finish of the BengalsRavens game on locker-room TVs, and then erupted.

“Everybody went crazy,” said Williams, who is in his 12th season with the Bills. “I’ve been a wreck for 10 to 15 minutes.”

His voice choked with emotion, and he wasn’t the only one.

“Well, I started crying, if that’s a good reaction...” former Buffalo running back Thurman Thomas said in a text.

Buffalo (9-7) will travel to face Jacksonville and former Buffalo head coach Doug Marrone on Sunday. Marrone resigned as the Bills’ head coach three years ago Sunday.

The Bills’ joy was tempered by the loss of 1,000-yard rusher LeSean McCoy with a right ankle injury. He was carted off the field in the third quarter and was in a walking boot after the game.

The frustration of a disappointing season got the best of the Dolphins (6-10) with 6:21 left, when receiver Jarvis Landry, running back Kenyan Drake and offensive lineman Jake Brendel were ejected following a fight. Landry was cited for disrespecting an official, and Drake for throwing his helmet 20 yards in anger. Unsportsmanlike-conduct penalties were called against both teams.

The Dolphins, who came into the game with the second-most penalties in the NFL, had 14 for 145 yards.

Meanwhile, for the Bills, 17 seasons of frustration ended.

“The locker room is electric, man,” said guard Richie Incognito, who finished a season above .500 for the first time in his 11-year career. “We have been working so hard for this. So much has been said about it, and now the monkey is off our back. We’re in the postseason, and we’ve got new life.”

Buffalo punctuated its victory with a 1-yard touchdown run by Williams, the first score of his career.

“I thought, ‘Try not to screw it up. They’re not going to call it again if I screw it up,’ ” he said.

He and his teammates celebrated with choreographed back flops in the end zone.

Jack Nicklaus wore Bills gear and a smile watching from the stands as his grandson, tight end Nick O’Leary, caught Tyrod Taylor’s 26-yard touchdown pass.

The Dolphins scored a touchdown with 1:56 left and recovered the ensuing onside kick, but Jordan Poyer’s interception sealed the win.

Taylor went 19-for-27 for 204 yards and one score. The Dolphins’ David Fales, a San Jose State alum, went 29-for-42 for 265 yards with one touchdown and one interception. He also ran for a score.