The Englishman was out in the fourth group of the day, starting on the back nine, and he took full advantage of early conditions in the United Arab Emirates to deliver a birdie frenzy and celebrate Fire Course's debut on the European Tour in sensational style.
Wednesday marked the 49th UAE National Day and Emirati invitational golfer Ahmed Skaik hit the opening tee shot to start the new event at Jumeirah Golf Estates before Sullivan made his charge up the leaderboard.
An opening birdie at the tenth was followed by another at the 12th to get his round under way before carding successive pars.
He soon took sole charge of the scoreboard as he wrapped up his front nine with four successive birdies from the 15th to reach the turn in 30 and sit at the summit on six under par.
Frenchman Antoine Rozner - who teed off in the second group of the day - was the closest challenger at five under following gains at the first, fourth, fifth, seventh and tenth but Sullivan's birdie trail did not stop there.
He rolled in another at the first and when he carded his sixth in a row at the second, he was at eight under.
Rozner temporarily joined him at the top after birdieing the 12th and an eagle at the par five 13th, but four time European Tour winner Sullivan nudged ahead with a serious possibility of a 59 on the horizon.
Back to back birdies at the fourth and fifth saw him reach ten under, with Rozner still on his coattails when he carded his ninth gain of the round at the 16th to finish at nine under.
Sullivan needed to finish his final three holes in three under to become only the second person to record a 59 in European Tour history - after Oli Fisher at the 2018 Portugal Masters.
His chances were boosted as he carded his 11th birdie of the day at the par five seventh, but could only roll in a par at the eighth.
Sullivan still had the chance to make history at the par four ninth if he holed out in two and he pushed his tee shot into the rough.
He produced a fine approach, which checked back and headed towards cup before settling seven feet away, however, Sullivan could not drain the birdie putt as he carded a stunning 61.
Fellow Englishman Matt Wallace moved into early contention to join Rozner at nine under following a superb final 11 holes.
Starting on the back nine, he traded a birdie at the 12th with a bogey at the 13th before he got hot just before the turn. A birdie at the 17th was followed by an eagle at the 18th to get to three under.
Wallace continued the surge with a gain at the first before a hat-trick of birdies from the third saw him move to seven under.
He picked up another shot at the seventh and finished his round with a birdie putt from the fringe at the ninth to sit alongside the Frenchman in the clubhouse in a tie for second.
Lorenzo Scalise, who was five under through seven, sits fourth at seven under with two holes remaining.