The 46-year-old wowed fans at the Traveler's Championship after shooting a round of 12 under par at TPC River Highlands in Connecticut.
The American is the second player to card 58 on a major tour, joining Japan's Ryo Ishikawa, who achieved the feat in 2010 at the Crowns tournament on the Japan Tour.
"It's pretty cool," Furyk told Sky Sports 4. "Winning a major championship is at the top of my list, playing and winning on Ryder Cup teams and Presidents Cup teams and winning golf tournaments. This is really special.
"A million and a half rounds played in the history of the PGA Tour and you look at the great names ahead of me. It's humbling, to stand alone at 58 is really a cool accomplishment."
Furyk made 10 birdies and an eagle in his round, completing the opening nine holes in a course-record 27 shots.
Pennsylvania-born Furyk, a 17-time winner on tour, carded a round of 59 in 2013 at the BMW Championship.
Al Geiberger in 1977 was the first to card a round of 59 on the PGA Tour, followed by Chip Beck (1991), David Duval (1999), Paul Goydos (2010) and Stuart Appleby (2010).
While Furyk took the headlines, it was Scotland's Russell Knox who won the tournament.
Knox recorded a final round of 68 to finish at 14-under-par to finish one shot clear of Jerry Kelly.
