He finished the game completing 16 of 31 passes for 199 yards with three touchdowns and no interceptions - and moved to 8-5 since inheriting the Gamecocks' starting quarterback job midway through the 2016 season.
It was Brunson's first-career fumble recovery and touchdown.
Matt Jones, Arkansas's starting quarterback from 2002-2004, is pretty much done with Bret Bielema after the Razorbacks' blowout loss at SC.
"It was quite weird at first, but I got used to it", Williams said of playing against his old teammates.
Bentley capped the drive with an 18-yard touchdown pass to Edwards, twisting high in the air for a jump ball in the back right corner of the end zone four seconds before halftime.
A sack of Allen by Dante Sawyer on the Razorbacks' next drive jarred the ball loose, and linebacker T.J. Brunson raced 73 yards with the recovery to make it 34-10 SC.
Wisconsin scores final 21 to beat Nebraska
In fact, after Nebraska tied the game at 17-all after Williams' reception return, the Badgers threw the ball only once. Wisconsin answered immediately when Taylor took an inside run to the house from 75 yards out.
The Gamecocks broke a 10-point game open in the third quarter.
"We just have to have a complete game each week", linebacker Skai Moore said.
Three touchdowns from the defense isn't likely to be a formula the Gamecocks can duplicate in the coming weeks, but Saturday it was exactly what they needed.
SC quarterback Jake Bentley threw three touchdown passes while completing 16 of 31 pass attempts for 199 yards.
Arkansas sophomore backup defensive end Briston Guidry, who had three tackles in the first four games, didn't travel with the team to SC.
Rico Dowdle had his best game of the year, running hard on 11 carries for 61 yards and looking like the weapon he was down the stretch last season.
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A loss would have left the Gamecocks "Free Fallin'" toward the second half of the season.
"Inexcusable coaching is what it is", Muschamp said.
It's probably not what David Williams had hoped for in his return back to Williams-Brice Stadium.
"No, that was dumb (bleep)", Muschamp said.
The Gamecock team that left College Station in a shroud of doubt is back on track to win seven or eight regular-season games.
The Razorbacks joined the club when sophomore walk-on Connor Limpert hit a 48-yard attempt to tie the game 3-3 in the first quarter. Had Williams not stepped out of bounds, that reception could have also been a touchdown for the Razorbacks. The Taxslayer, Citrus and Orange bowls had reps to watch the game.
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Certainly no need to adjust the added swagger the SC defense gained Saturday.