ORCHARD PARK, N.Y. -- Jay Ajayi jump-started the Miami Dolphins' sputtering season two months ago and continues to be the engine driving the team's playoff push.

Ajayi rushed for 206 yards and a touchdown in Miami's 34-31 overtime victory over the Buffalo Bills on Saturday. His biggest run, a 57-yarder on the first play of the Dolphins' final drive of overtime, flipped the field and set up Andrew Franks' 27-yard winning field goal with 47 seconds remaining.

The Dolphins (10-5) have won three in a row and nine of 10 since Ajayi took over as the starting running back, putting them on the verge of making the playoffs for the first time since 2008. Miami can clinch a wild-card spot with a victory next week against New England, or a Kansas City win over Denver on Sunday.

Ajayi became the fourth player in NFL history to rush for more than 200 yards three times in one season. He had 204 yards in his breakout game against the Steelers in Week 5 that started the Dolphins' surge and 214 versus Buffalo the following week.

"He's a grinder, he's a workhorse," Dolphins tight end Dion Sims said. "He goes 100 miles an hour and that's why he's got the nickname "train" because he is just going nonstop."

Franks forced overtime when he made a career-long 55-yard field goal with 6 seconds left in regulation. The Dolphins led by 14 points on three separate occasions before the Bills scored 17 straight to take their first lead with 1:25 left in the game.

"I can't say enough about how our guys fought through," Dolphins coach Adam Gase said. "A lot of things we're going the way we wanted it to go and we just kept battling."

Matt Moore started in place of injured quarterback Ryan Tannehill (knee) for the second straight week and was 16 of 30 passing for 233 yards, two touchdowns and an interception.

DeVante Parker and Kenny Stills each caught a touchdown pass and rookie Kenyan Drake scored on a long run.

The loss eliminated Buffalo from playoff contention for the 17th straight season, extending the longest postseason drought in North American sports.

"Obviously a tough day to say the least," Bills coach Rex Ryan said. "Our guys fought their butts off and at the end of the day it wasn't enough."

The Bills got the ball first in overtime and reached the red zone before former Dolphin Dan Carpenter missed a 45-yard field goal attempt wide right.

Miami advanced to the Buffalo 45 before punting on its first overtime possession. The Bills punted from their own 41 on their next drive.

Franks atoned for hitting the upright on a 46-yard attempt earlier in the fourth quarter with his 55-yard kick. Bills players and coaches complained that they tried to call timeout before Franks' kick.

"The guy on the sideline who was standing next to coach (Rex Ryan) said that coach Ryan had not called timeout before the snap," referee Craig Wrolstad told a pool reporter. "That is why they were not allowed a timeout."

The Bills set a franchise record with 589 yards of offense.

Tyrod Taylor completed 26 of 39 passes for a career-high 329 yards and three touchdowns. He also rushed for 60 yards and broke his own franchise record for quarterback rushing with 580 yards this season.

LeSean McCoy had 128 of the Bills' 272 rushing yards. Mike Gillislee rushed for 35 of his 91 yards in overtime.

Sammy Watkins had seven receptions for 154 yards and a touchdown. Former Dolphins tight end Charles Clay caught eight passes for 85 yards and scored twice for the first time in his two seasons with the Bills.

Taylor threw his second touchdown pass of the day to Clay to cap an 89-yard drive after Carpenter's 28-yard field goal brought the Bills within 28-24 at 5:51 of the fourth quarter.

The two teams combined for 305 yards and four touchdowns during a thrilling third quarter.

Parker caught a short pass over the middle and bounced off a would-be-tackler on his way to a 56-yard touchdown that extended the Dolphins' lead to 21-7 three minutes into the second half.

McCoy made it 21-14 with his 19-yard touchdown run, but the Dolphins went back up by two touchdowns on Moore's 6-yard pass to Stills.

The Bills responded quickly, driving 78 yards on four plays and cutting the lead to 28-21 on Taylor's 18-yard touchdown pass to Clay.

Ajayi rushed for 81 yards in the first half, exceeding his total from each of the last six games, and the Dolphins led 14-7 at halftime.

Ajayi had 47 yards of his yards in the first quarter and gave the Dolphins' an early lead when he broke two tackles on a 2-yard touchdown run. On the Dolphins' next drive, Drake circled out of an inside run and sprinted 45 yards up the sideline to make it 14-0 early in the second quarter.

Buffalo got on the scoreboard with 5:06 left in the second quarter when Watkins hauled in a 38-yard touchdown pass from Taylor. Carpenter missed a 46-yard field goal in the first quarter.

Miami squandered a scoring chance late in the first half when Moore was intercepted in the end zone by Corey White.

NOTES: CB Byron Maxwell (ankle) and LB Jelani Jenkins (knee) missed the game for Miami. ... The Bills were without LT Cordy Glenn (back). ... Hall of Fame quarterbacks Dan Marino and Jim Kelly attended the game. Kelly was joined on the sideline by his nephew, Ole Miss quarterback Chad Kelly.