The 20-year-old phenom fired an eagle and eight birdies to card a 10-under-par 62, breaking the previous course record of 63.
American Kevin Roy, 35, matched Potgieter's feat, also carding an eagle and eight birdies to join the South African at the top of the leaderboard.
Both players are chasing their maiden PGA Tour wins and lie one shot clear of Australian Min Woo Lee and Americans Max Greyserman and Mark Hubbard.
Starting from the 10th, Potgieter opened with a birdie at his first hole and never looked back. Further birdies followed at 12 and 14 before he caught serious fire on the 16th with a birdie-eagle-birdie-birdie run.
He reached 10-under with back-to-back birdies at seven and eight, but couldn't hole a 12-footer at the last to grab the outright lead.
"I was standing on the last hole and I looked at the leaderboard and saw someone else at 10, so I was real eager to make that putt at the last," he said after settling for a tap-in par.
Potgieter, already one of the longest hitters on the PGA Tour despite being only 20 years old is chasing a first PGA Tour title after coming close in February when he lost to Brian Campbell in a playoff at the Mexico Open.
Andrew Putnam was alone in sixth on 64, followed by a large group of seven players tied on 65.
South Africa's Aldrich Potgieter remains in the hunt for his maiden PGA Tour title at the Rocket Classic, although the tournament has a new trio of leaders at the halfway mark.
When Keegan Bradley was announced as the new Ryder Cup captain in July last year, the second question he faced was whether he would consider giving himself a pick for the matches at Bethpage in September 2025.
Keegan Bradley edged Tommy Fleetwood with a birdie on the final hole to win the Travelers Championship in dramatic fashion on Sunday.
Tommy Fleetwood has a three-shot lead going into the final round of the Travelers Championship on Sunday.
