Saunders, 30, closed with six straight birdies at Atlantic Beach Country Club -- the Jacksonville-area club where he has a membership -- for the seventh sub-60 round in Web.com Tour history.
With wife Kelly and 8-year-old son Cohen looking on, Saunders made an 18-foot birdie putt on the par-3 eighth and closed with a 10-footer on the par-4 ninth.
"It was dead center. I saw it going in from a few feet out," he said about the final putt.
Stephan Jaeger set the tour record of 58 last year in the Ellie Mae Classic at TPC Stonebrae in Hayward, California, and Notah Begay III, Doug Dunakey, Jason Gore, Will Wilcox and Russell Knox also shot 59.
"Honestly, I was excited because my wife and my son, Cohen, who is really getting into golf, got to watch," Saunders said. "He's only watched me play three full rounds of golf probably. He's watched me fail in golf a lot, which is good, that's a good lesson for him. For my wife, Kelly, to be there; she's watched the ups and downs of this whole deal. I'm really glad that they got to be out there and watch me do that."
This week marks the one-year anniversary of the death of Saunders' grandfather, golf legend Arnold Palmer, who died a year ago Monday at age 87.
Saunders had 13 birdies and a bogey. Opening on the 10th hole, he birdied the first three holes, added a birdie on 14, bogeyed the par-3 15th and birdied 15 and 18 to make the turn in 5 under. He birdied No. 2 and Nos. 4-9 for a 7-under 28 on his final nine.
On the par-3 fifth, the 30-year-old former Clemson player holed a 40-footer from well over the green with a shaved bank and pond looming beyond the hole.
"You're dead. You've got no shot there," Saunders said. "I putted it up the hill and it was going Mach 1, it would've been 30 feet past the hole and it hit dead center."I was just hoping for it to hit the pin. When I saw it was about 2 feet away, my heart rate went down thinking I was at least going to hit the pin. Then it when it went in I was embarrassed because it was a horrible shot, but you need to get some luck sometimes."
Saunders is trying to regain his PGA Tour card in the four-event Web.com Tour Finals after finishing 129th in the FedEx Cup standings. He entered the week 24th in the race for 25 PGA Tour cards with $27,900 in the first three events. He tied for 11th in the Nationwide Children's Hospital Championship, tied for 40th in the Albertsons Boise Open and missed the cut in the DAP Championship.
"I've been pretty tired in these Web.com Tour Finals, so it was nice to get home and get some rest and not over-practice coming in," Saunders said. "But, on Tuesday I had a really good warm-up session and was able to figure things out. It comes back to putting, and I made everything today. That's how you go low."
"It was a good time out there and it was a real special day, certainly memorable. I played with my buddy Steve Wheatcroft and we kind of fed off each other," Saunders said. "Honestly, it just felt like a regular day at home playing our little money game and I got into a good rhythm. It was a blast."
Wheatcroft entered the week 23rd with $29,025 after finishing 179th in the FedEx Cup standings.
Tyler Duncan and Ben Silverman shot 63.
Duncan came into the tournament 13th with $43,158, more than enough to secure a card. Atkins and Silverman have already earned PGA Tour cards as top-25 finishers on the Web.com Tour's regular-season money list. They are trying to improve their status.
The Associated Press contributed to this report.