Bill Haas had a 70 and was in second place while Chad Campbell moved into contention with a 64 that left him three strokes behind at 10 under. He was tied with Shaun Micheel and Johnson Wagner, both shooting 68s.
Branshaw, Haas and Wagner are seeking their first PGA TOUR victories, while Campbell and Micheel are trying to turn around their games.
Two-time champion Fred Funk led a group of nine that sat four back at 9 under and six others were 8 under and well in contention.
Branshaw took the lead Friday as most players struggled with changing course conditions at Annandale Golf Club, where frequent rain this week gave way to sunny skies and a persistent wind that dried the greens.
He made 11 straight pars Friday, then finished with two birdies for a 68. He opened the Classic with a 66. Branshaw, a 37-year-old golfer from Tampa, Fla., in his third full year on tour, had been bogey-free through 44 holes before making one at No. 9 Saturday. But he had four birdies on par-4 holes and again put together a string of pars, finishing his round with five straight.
Haas, the son of longtime PGA and Champions tours veteran Jay Haas, missed a 9-foot birdie putt at 17 that could have reduced Branshaw's lead. He had three bogeys but he made four birdies, including 13-foot putts on Nos. 2 and 11 and a 12-footer on No. 15.
Campbell said his goal is to make a significant move up the money list. He started his career with four straight top-30 money list finishes and wants to end his fifth year on tour that way. After finishing 14th last year, he's 82nd and needs more than $1 million in his final three appearances of the season to reach that goal.