The Bills (5-10) came into the game assured of missing the playoffs for the 13th consecutive season.
While Bush led an efficient offense, safety Reshad Jones recovered two fumbles and made an interception at the Miami 1 with 71 seconds left to seal the victory. The Dolphins forced four turnovers playing with a patchwork secondary that included starting cornerback Dimitri Patterson, acquired Tuesday after being waived by Cleveland.
Bush's first TD catches of the year covered 17 and 12 yards from Ryan Tannehill, helping Miami build a 24-3 lead. Bush also ran for 65 yards, including a 1-yard touchdown.
The Dolphins took advantage of Buffalo's woeful run defense by netting 182 yards on the ground while averaging 5.2 per carry. Backup Lamar Miller had 73 and Tannehill added 44, including 31 on a dash that set up a touchdown.
Miami went 7 for 14 on third down and didn't commit a turnover. Tannehill threw for only 130 yards but had a passer rating of 93.8.
The Dolphins had three fumble recoveries, doubling their season total, but their most spectacular takeaway was Jones' interception. With the Bills at the Miami 1 and 80 seconds left, Jones leaped at the line of scrimmage to snare Ryan Fitzpatrick's pass and clinch the win.
The Dolphins' flurry of takeaways came after they had one in their previous seven games.
Nate Kaeding, signed during the week by Miami, made a 45-yard field goal but had a 46-yard try blocked by Alex Carrington.
Buffalo's C.J. Spiller ran for 138 yards, but missed chances hurt the Bills. Stevie Johnson lost a fumble at the Miami 17 and dropped a pass in the end zone, when Buffalo settled for a field goal. That came after C.J. Spiller's career-best 62-yard run.
The Dolphins led 24-3 in the fourth quarter before the Bills mounted their only touchdown drive.
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