The Dolphins defense had no answers for the passing of Brew Bledsoe and also didn't help their cause with three turnovers, giving them nine in their two losses against Buffalo this season.
Momentum in the game swung back and forth a couple of times, with the Dolphins dominating early, Buffalo coming on and taking the lead at halftime, the Dolphins seemingly taking charge again late in the third quarter before the Bills took control for good.
Buffalo scored the last 21 points in the game after Williams' career-best 55-yard touchdown run on a third-and-1.
But three plays later, Bledsoe connected with Peerless Price on a 73-yard touchdown to give Buffalo a 28-24 lead.
The Dolphins then marched into Bills territory, but tight end Randy McMichael made a rookie mistake when he stretched the ball with one hand on a third-down pass that was going to fall short of the first-down marker no matter what.
As McMichael held the ball away from his body, it was batted away by Bills defensive end Kendrick Office, who also recovered the fumble at the 43-yard line.
On the very next play, Bledsoe threw a bomb in Eric Moulds' direction, but Sam Madison was in great position to make the interception, except that he had to stretch for it. He couldn't bring it down and wound up tipping it right to Moulds, who strolled into the end zone for 57-yard touchdown to make it 31-21.
The Dolphins again marched into Buffalo territory, but this time the ball slipped out of Jay Fiedler's hands as he was throwing a pass, it floated into the air and landed into the arms of Bills cornerback Nate Clements.
A 47-yard pass from Bledsoe to Moulds gave the Bills a first-and-goal at the 3-yard line and Travis Henry — who again rushed for over 100 yards against the Dolphins — punched it in on third-and-goal from the 1-yard line to apply the knockout punch midway through the fourth quarter.
By this time, Williams already had set the single-game rushing record.
Williams' great day began with a 45-yard touchdown run on the Dolphins' first play from scrimmage as Miami grabbed a quick 7-0 lead.
After a Mike Hollis field goal made it 7-3, the Dolphins put together another touchdown drive the second time they had the ball, highlighted by a 17-yard run by Williams, a 17-yard completion to Jed Weaver, and a questionable pass interference penalty in the end zone on third-and-goal.
The score came when Ray Lucas, who left the game after suffering a "stinger" in the second half, faked a handoff to Williams and lofted a 1-yard pass to Weaver.
But that was one of the few successful passing plays for the Dolphins, who finished with a paltry 33 net passing yards.