Brown racked up 65 yards on 13 carries for Miami (1-0), which also got 62 yards on the ground from Ricky Williams on 18 attempts.
Dolphins signal-caller Chad Henne went 21-of-34 through the air, amassing182 yards for the victors.
The Bills (0-1) were led by quarterback Trent Edwards, who tossed for 139 yards on 18-of-34 passing, connecting on a fourth-quarter touchdown.
Chan Gailey marked his debut as Buffalo's head coach with a defeat.
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