ORCHARD PARK, N.Y. -- With one chase behind him, LeSean McCoy has another in his sights.

McCoy passed a personal milestone on Sunday, becoming the 30th player in NFL history to surpass 10,000 career rushing yards while helping the Buffalo Bills remain in the playoff chase with a 24-16 victory over the Miami Dolphins at New Era Field.

"My whole mindset was, let's get the win, and let's get 10K," a smiling McCoy said during his postgame remarks while wearing a blue sweatshirt with "WE CHASING 10K" emblazoned on the front. "I'm happy it's over. I'm happy it's done. Now I look forward to trying to get in these playoffs."

McCoy compiled 96 total yards (50 rushing, 46 receiving) and two touchdowns as the Bills improved to 8-6 for just the third time in the 18 years since the team last reached the postseason.

Several of McCoy's teammates wore matching sweatshirts to the game and took pride in helping him conclude his season-long 10K chase.

"It's so cool to share that with Shady and the guys on this offensive line," guard Richie Incognito said. "What we've been doing here for the last three years is really special running the football."

Bills quarterback Tyrod Taylor returned after missing one game with a bruised knee and completed 17 of 29 passes for 224 yards and a touchdown to McCoy. Taylor also ran for 42 yards and another score.

The loss diminished the Dolphins' playoff chances following an upset win over the New England Patriots last Monday night. Jay Cutler completed 28 of 49 passes for 274 yards but threw three interceptions for Miami (6-8). Kenyan Drake ran for 78 yards and a touchdown, and Cody Parkey kicked three field goals.

"We didn't do anything really well today," Dolphins coach Adam Gase said. "I can't say we were doing things wrong, it was just they played better than us."

Miami scored the only 10 points of the fourth quarter to make things interesting.

Drake's 1-yard touchdown run to cut the Bills' lead to 24-13 with 7:57 remaining in the fourth. The Dolphins' scoring drive was extended by an unsportsmanlike-conduct penalty on Buffalo's Adolphus Washington for swiping at Drake out of bounds after the Bills' defense made a stop on third-and-goal from the 1.

Parkey made a 27-yard field goal with 37 seconds left, and punter Matt Haack recovered an onside kick at midfield. However, Buffalo rookie cornerback Tre'Davious White intercepted Cutler on a deep pass to seal the victory.

Shareece Wright's 49-yard interception return -- which included the cornerback recovering his own fumble at the end of the run -- set up Stephen Hauschka's 34-yard field goal that made it 24-6 late in the third quarter. Safety Jordan Poyer also intercepted Cutler.

"We just made too many mistakes," Dolphins defensive lineman Ndamukong Suh said. "We allowed them to move the ball, especially early, give them their momentum, and we can't allow teams to do that. We've got to be able to get off the field. We did a little bit better job in the second half, but we've got to clean it up."

Taylor led an 80-yard drive in the final two minutes of the first half and scored on a 9-yard run just before the break for a 21-6 lead.

McCoy scored Buffalo's first two touchdowns, pushing his career total to 81 and moving into the top 60 on the NFL's all-time list.

Having gotten the wind knocked out of him on a 14-yard run that put him over 10,000 yards for his career, McCoy returned two plays later to catch a 16-yard touchdown pass in the corner of the end zone that put the Bills ahead 14-6 in the second quarter.

"We didn't think we'd get a linebacker guarding me," McCoy said. "I looked at Tyrod like, this is a surprise. An early Christmas present."

The Bills never trailed after scoring a touchdown on their opening possession for the first time this season. McCoy's 4-yard run capped an 81-yard drive.

NOTES: Bills RB LeSean McCoy moved past Ricky Williams for 29th on the NFL's all-time rushing list with 10,011 yards. He went over 10,000 yards on 2,145 carries, fewer than all but four other running backs: Jim Brown, Adrian Peterson, Barry Sanders, O.J. Simpson. ... Bills CB E.J. Gaines left the game in the third quarter with a knee injury and did not return. WR Kelvin Benjamin (knee) started after being listed as questionable. ... Dolphins S T.J. McDonald sustained a shoulder injury in the fourth quarter. DE Andre Branch (knee) and CB Cordrea Tankersley (ankle/shoulder) were inactive. ... Buffalo plays its final two games at New England (Dec. 24) and at Miami (Dec. 31). The Bills went 6-2 at New Era Field this season for their best home record since 1999. ... Dolphins WR Kenny Stills and TE Julius Thomas kneeled during the national anthem. ... Bills TE Charles Clay caught five passes for 68 yards against his former team.