The Dolphins had one last shot from the Buffalo 47-yard line, but Gus Frerotte was sacked on back-to-back plays to end the game.
Brown's fumble was the Dolphins' fifth turnover, two fumbles and three interceptions.
Making matters worse were a franchise-record 18 penalties, which cost the Dolphins 102 yards and also gave the Bills too many cheap touchdowns.
But while the Dolphins' execution left much to be desired, you can't question their grittiness after they clawed their way back.
The Dolphins finally got on the scoreboard in the third quarter when Frerotte hit backup tight end Will Heller with a 1-yard touchdown pass.
Frerotte then hit Randy McMichael for a 30-yard touchdown midway through the fourth quarter to make it 17-14.
But, typical for this day, McMichael drew a taunting penalty on his touchdown for sticking the ball out at safety Lawyer Milloy as he crossed the goal line.
So Olindo Mare had to hit the ensuing kickoff from his 15-yard line, and Terrence McGee took it back 52 yards to the Dolphins 33-yard line.
The defense, which started slowly but was tremendous in the second half, forced Buffalo to settle for a field goal and the Dolphins were without six points as they took over with a little over four minutes left.
But on second-and-6 from the 25, Brown fumbled as he was fighting for extra yardage to stop the drive. The play was reviewed, but replay seemed to show that Brown lost control of the ball -- after a hit by Bills cornerback Nate Clements -- before his knee hit the ground.
It was a disappointing way to end the game for Brown, who had several nice runs and finished with over 100 yards for the second consecutive game.
There was not one single Dolphins player who had a good first half, however.
On the first play from scrimmage, Kevin Carter was flagged for offside and it was a sign of bad things to come.
Buffalo marched 67 yards on that drive, which ended with Willis McGahee's 1-yard touchdown run.
A defensive holding penalty on Vonnie Holiday helped Buffalo on its next drive, but the Dolphins got a victory of sorts when they forced the Bills to settle for a field goal after they had a first-and-goal from the 1.
After a bad snap led to a fumble by punter Donnie Jones, Buffalo had to march only 45 yards on its third possession, which ended with a 2-yard touchdown pass from Kelly Holcomb to Eric Moulds. The Bills got two first downs on the drive on penalties, including a defensive holding on Donnie Spragan that nullified a sack that would have forced Buffalo to go for a field goal attempt.
On the flip side, the Dolphins could get nothing going offensively in the first half and the best drive ended when Frerotte was intercepted by McGee in the end zone.
Frerotte and his teammates finally showed some life in the second half, but in the end it was a case of one too many mistakes for the Dolphins.