The 43-year-old American hit a gap wedge to three feet on his final hole, the par-four ninth, and calmly sank the putt for a magical 12-under-par 59 to end a breezy day at Conway Farms Golf Club tied at the top with compatriot Brandt Snedeker.
Furyk piled up 11 birdies, one bogey and an eagle at the par-four 15th as he rebounded in astonishing fashion from an opening 72 to post an 11-under total of 131 in the third of the US Tour's four lucrative FedExCup play-off events.
In pursuit of his first victory on the US circuit since the 2010 Tour Championship, Furyk was level with first-round leader Snedeker, who carded a 68.
Zach Johnson (70) was alone in third at eight under, two strokes better than fellow Americans Nick Watney (69), rookie sensation Jordan Spieth (65), Ryan Moore (69) and Kevin Streelman (70), and South African Charl Schwartzel (70).
World number one Tiger Woods ended a frustrating day with a 72 in a tie for 13th at four under, after being docked two strokes due to his ball moving on his opening hole.
The infringement occurred on the par-four first where Woods struck his second shot over the back of the green, then tried to remove a loose impediment before playing his third.
Though Woods felt his ball had only oscillated before he ran up a double-bogey six there, video footage later proved that it had shifted position and his score was amended to a quadruple eight.
The biggest roars of the day, from galleries lining both sides of the fairway, were directed towards Furyk as he walked on to the ninth green after hitting a superb approach from 103 yards.
After he had knocked in the three-footer to complete a magical 59, the crowds erupted in delight. Furyk pumped his right fist on delight, acknowledged the fans, then hugged his long-time caddie Mike "Fluff" Cowan.
"Pretty exciting day," Furyk said after setting up his astonishing round with an explosive outward nine of eight-under 28 that included his eagle at the 15th where he holed out from 115 yards in the fairway.
"I guess the moment kind of struck me the most at No. 9 when I hit the iron shot, when I hit the wedge shot in there close, and the crowd erupted and I started looking around.
"It just hit me how many people had come over to that side to see the finish and how excited the crowd was. It was kind of like winning a golf tournament to be honest with you, is the reaction I got."
The five players who had previously shot 59s on the US Tour are Americans Al Geiberger (1977 Memphis Classic), Chip Beck (1991 Las Vegas Invitational), David Duval (1999 Bob Hope Classic) and Paul Goydos (2010 John Deere Classic) as well as Australian Stuart Appleby (2010 Greenbrier Classic).
Northern Irish world number four Rory McIlroy, the defending champion, battled to a six-over-par 77 to end the second round stone last in the elite field of 70.
"I'm just not scoring well," the 24-year-old said. "I missed it on the wrong side, I'm missing greens with wedges, and just don't have my scoring hat on. I feel like I'm hitting the ball pretty well, I'm just not scoring."
Seventy players have qualified for the elite BMW Championship, the US Tour's penultimate play-off event, and any improvement in the overall FedExCup points standings after Sunday's final round could be crucial.
Of the 30 who advance to next week's season-ending Tour Championship, any of the top five would automatically clinch FedExCup honours and a staggering $10 million bonus with victory in Atlanta.