Branshaw stands at 9-under-par 204 for the tournament, one stroke clear of first-round leader David McKenzie (69) at Redwood Meadows Golf and Country Club.
Co-overnight leader Peter Tomasulo, who shattered the course record by four strokes with a 61 on Friday, struggled to a 1-over 72 in his third round and leads a group of three golfers tied for third place at minus-7.
Tomasulo is joined in third place by Aaron Barber, who carded the day's low round at 7-under 64, and Erik Compton (69).
Branshaw, who shared the overnight lead with Tomasulo and Kevin Johnson, hit just four of 14 fairways in his third round and mixed four birdies with three bogeys.
He was 11-under-par through 15 until two bogeys on his final three holes opened the door for the rest of the field. All in all, there are 17 players within six shots of Branshaw heading into Sunday.
'Overall, it was just okay,' Branshaw said of his round. 'It was going okay until the last three holes.'
If Branshaw reaches the winner's circle, it will be for just the second time on the Nationwide Tour -- and the first time since his only title at the 2002 Gila River Classic.
The victory would also likely ensure the 35-year-old American a top-20 finish on the money list, and thus a PGA Tour card for the 2006 season.
'We'll see what happens tomorrow,' said Branshaw, whose best finish this year was a tie for third place at the Virginia Beach Open. 'It all depends on the weather.'
Branshaw, who leads the field in putting, opened his round by rolling in a 15- footer for birdie at the first hole. He gave that shot back with his first bogey of the day at No. 2, but then collected two more birdies to make the turn at minus-10.
A 15-foot birdie putt at the par-4 12th moved Branshaw to 11-under before his late collapse. He three-putted for bogey at Nos. 16 and 18 to fall to minus-9.
'The wind affected me down the stretch,' admitted Branshaw. 'After seeing where the pins have been the past three days...you've got to control your irons pretty well.'
McKenzie entered the third round tied for fourth place at 6 under. He moved one shot further into red numbers after carding three birdies and two bogeys on the front nine, but fell back to minus-6 with a bogey at the par-4 10th.
The Australian got two shots back with birdies at his last two holes.
Barber's 64 included eight birdies and just one bogey, which came with a three-putt at the 16th. His eight birdie putts averaged more than 11 feet, including a 25-footer at the par-4 ninth.
'It was a fine day,' said Barber. 'It is a tough enough golf course that you can get back into it with a good round...For the most part I gave myself a lot of good birdie putts.'
Johnson struggled to a 3-over 74 in his third round to fall into a tie for sixth place at minus-5. He is joined there by Nathan Green (68), Chad Collins (69) and Jason Schultz (71).
Cameron Percy (67), Alan McLean (70), Stephen Gangluff (70) and Keith Nolan (73) are knotted in 10th place one stroke further back.