So when the Bills cornerback saw the ball coming loose, he provided one last punch to pry it free.
"I've been trying to punch at it all day because that dude's a load," Clements said. "I just went for the ball and it came out."
It happened after the Dolphins overcame a 17-0 deficit and were threatening to pull ahead.
After marching the Dolphins 36 yards on seven plays, Gus Frerotte hit Brown with a short pass over the middle. Brown cut to his right and was caught from behind by London Fletcher. Clements ran up and stripped the ball before Brown was down, and Troy Vincent recovered on the Bills' 18.
"Today, our backs were up against the wall on several occasions and we did some good things," Vincent said. "They were in a position to score and we got a fumble -- it's always huge."
Chalk this win up to a banged-up defense that overcame its suddenly maligned reputation after allowing 1,054 yards in its last three games.
"This victory period is a big confidence boost," Clements said. "This is something that can start a snowball effect. ... For us to come out on top it's huge."
Clements' turnover was the fifth of the game for Buffalo (2-3) and helped snap the Bills' three-game losing streak.
The Bills offense also responded to a degree. Holcomb completed 11 of his first 15 attempts and engineered scoring drives on Buffalo's first three possessions.
Holcomb finished 20-of-26 for 169 yards passing and a touchdown. Willis McGahee had 86 yards rushing and a touchdown while Eric Moulds had 59 yards receiving and a TD. After scoring 17 points in the first half, the Bills were limited to Rian Lindell's 47-yard field goal.
The Dolphins (2-2), coming off a bye week, couldn't overcome their undisciplined play.
Miami committed a franchise-record 18 penalties for 108 yards. The costliest was a holding call against linebacker Donnie Spragan
that negated Vonnie Holliday's 8-yard sack on third down. The penalty gave Buffalo a first-and-goal at the Dolphins' 3, setting up Moulds' 2-yard touchdown catch that put the Bills up 17-0.
Linebacker Zach Thomas shook his head in frustration.
"We killed ourselves on defense, man," Thomas said. "Let them beat you, don't let yourselves beat you."
Coach Nick Saban wouldn't pin the blame on Brown's fumble, saying the Dolphins dug too big a hole for themselves in the first half.
"We need to improve our ability to play with discipline, especially on the road, especially in the beginning of games," Saban said. "That put us behind the 8-ball."
Limited to 106 yards in the first half, the Dolphins responded when Frerotte hit Will Heller for a 1-yard touchdown pass 10 minutes into the third quarter. Frerotte then found Randy McMichael for a 30-yard TD with eight minutes left, capitalizing on McGahee's fumble at the Buffalo 35.
Frerotte went 21-of-33 for 226 yards, with two touchdowns and three interceptions. Brown had 97 yards rushing.
The Bills offense was just the opposite, looking strong in the first half under Holcomb, who threw in rhythm and relied mostly on quick outs or short throws over the middle, all things Losman appeared incapable of doing.
It was a big turnaround for a Buffalo offense that managed 29 points -- two touchdowns and five field goals -- in the last 14 quarters.
While pleased with Holcomb's outing, coach Mike Mularkey refused to say who his starter was for next week's game against the visiting Jets.
"We needed a win and this team understood it," Mularkey said. "We have to win close games at the end. And when we needed plays, guys made them at the end."
The Dolphins are 1-9 in their last 10 road games. ... McMichael has scored in four straight games, becoming the first Miami player to do so in a single season since Mark Clayton in 1988. ... Lindell also made a 24-yard field goal. ... Holcomb's first-half numbers alone -- 14-of-20 for 118 yards -- bettered what Losman managed in his last three outings. After throwing for 170
yards in a season-opening win against Houston, Losman had 113 against Tampa Bay and 75 each against Atlanta and New Orleans.