Six minutes after they won, the Dolphins (7-8) were eliminated from playoff contention when Cincinnati beat Pittsburgh.
The Bills (5-10) came into the game assured of missing the playoffs for the 13th consecutive year.
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 stymied Buffalo’s offense 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 season covered 17 and 12 yards.
Source: Associated Press