Branshaw leads D.A. Points and overnight leader Jason Gore by four shots. Points fired a third round 61, to become the third player in two days to shoot the course-record. Gore and Branshaw had set the mark on Friday.
Branshaw's 23-under score also matches the 72-hole tournament record set by last year's winner Ben Crane. The Buy.Com Tour record of 26-under-par, first set by Chris Smith at the 1997 Omaha Classic and matched by Todd Barranger at last year's Dayton Open, is within reach.
Patrick Sheehan, who had set the old course record of 62 on Thursday, is alone in fourth place at 18-under-par 195. Brad Fabel, James McLean and Barranger are tied for fifth at minus 16.
The leader's round started slowly as he was just 1-under through five holes, thanks to a birdie at the third. Branshaw's round took off with a 30-foot eagle at the par-5 sixth. He then birdied the next two holes to help him make the turn at 5-under.
'That one got me going. It definitely kick-started my round,' said Branshaw of his eagle. 'Anything can happen tomorrow. Four shots could be gone in a couple holes.'
Branshaw's lone mistake was at the 10th, where he bogeyed due to an errant tee ball. He atoned for that mistake at the next. The former Arizona Wildcat later sank a 35-footer for birdie on 15 before a kick-in birdie at the par-5 17th.
'It feels good. I'm just having fun out there,' said Branshaw, who has made just 10 of 23 cuts this season. 'I didn't even know what I was shooting out there. On 17, I tried to figure out what my score might be. I do know I made my first bogey of the tournament. As for tomorrow, you just have to believe in yourself and believe you can hit the shots you need to hit.'
Points, who hasn't carded a bogey since Thursday, got his round going with a birdie at No. 5. He then eagled the par-5 sixth, before his final birdie on the front side at eight.
After making the turn, Points had a birdie explosion. He birdied the 10th, then started a string of three straight birdies on 12. He parred the 15th and 16th, before consecutive birdies starting at 17 to close out the round of 61.
'Not starting out with birdies was tough because those holes are fairly easy, but you have to be patient,' said Points the 2001 Inland Empire Open winner. 'All of a sudden something clicks in your swing and a few putts go in. You get a little confidence and it snowballs on you. I needed to do this just to have a shot at it. I'm going to try and keep it going tomorrow.'
Gore, who has won twice on the Buy.com Tour this season, had an up-and-down round of 69. He carded three birdies on the front nine, but also had a pair of bogeys. On the back side, he posted three more birdies, but started with a double-bogey at the par-4 10th. It was his playing partners round that most impressed Gore.
'David (Branshaw) played great today,' Gore said. 'If he plays like that tomorrow, he's going to be tough to beat. Four shots isn't a lot out here. I didn't kill myself, but I didn't put myself in prime position either.'
Gore is one of the four two-time winners on the Buy.Com Tour this season. He and Patrick Moore, who is tied for 21st at minus 13, join Cliff Kresge, who is tied for 27th at 12-under, and Arron Oberholser, who missed the cut, as the two-time winners this season.
If one of those were to comeback and win to become a three-time winner, that person would get the automatic Battlefield Promotion to the PGA Tour. Four players have previously gained this promotion -- Smith in 1997 and Heath Slocum, Chad Campbell and Pat Bates in 2001.
Full-field scores from the Gila River Classic