First-round leader Bryson DeChambeau only made it to the turn, while the threesome of Masters champion Jordan Spieth, four-times major winner Rory McIlroy and world number six Rickie Fowler walked off after 13 difficult holes that yielded just four birdies between them.
Sullivan (67) was unperturbed, however, picking up shots on his first three and last three holes to reach the tournament's half-way stage on 10 under.
"My putter was getting hot early doors and I lost my way in the middle. I'm really happy with the fight back at the end," Sullivan told reporters.
Abu Dhabi HSBC Golf Championship
McIlroy joins Fowler among Abu Dhabi leaders
23/01/2016 AT 16:00
DeChambeau is a stroke adrift, while four players -- Joost Luiten, Rafael Cabrera-Bello, Thomas Bjorn and Richard Bland -- are on seven under. The latter two have seven holes to play.
Physics student DeChambeau, resuming on eight under, rolled in eight and 20-foot birdies on his first and third holes to reclaim joint leadership, the eccentric amateur later grinning as he doffed his flat-cap and whipped up the crowd.
Yet a bogey at his last after finding the bunker dragged the Californian back to nine under.

Referee Mark Litton talks with USA's Jordan Spieth, USA's Rickie Fowler and Northern Ireland's Rory McIlroy

Image credit: Reuters

"The last was kind of a killer, but it's golf. I've just got to learn from it and say, hey, got to hit the fairway next time," said DeChambeau, who is unusual in playing with clubs of all the same length. "I didn't have my A-game today."
The 22-year-old was unperturbed by the prospect of playing 27 holes on Saturday and will resume at the first tee after starting from hole 10.
"It's just like a new round, I'm not worried about it," he added.
Resuming on six under, McIlroy, 26, must have fancied his chances of reeling in Sullivan, but the Northern Irishman struggled with the putter.
He made par on the first eight holes, a sequence that ended with a bogey on nine, and was grim-faced after missing birdie chances at 12 and 13.
McIlroy will start on five under, two clear of world number one Spieth who sunk successive bogeys at holes four and five before claiming a shot back at the par-five 10th.
He was fortunate on the ninth, his tee shot striking the rear of a spectator standing to the left of the fairway -- the ball was destined for the water but instead thudded into the rough and Spieth, 22, was able to scramble for par.
Fowler, who began the day on two-under, made three birdies in an unblemished display to pull level with McIlroy.
World number five Henrik Stenson carded four bogeys as the Swede slipped to four under with six holes to play.
Abu Dhabi HSBC Golf Championship
McIlroy: Majors more important than Olympic gold
20/01/2016 AT 16:00
Golf
'I'll try to not be as animated' - McIlroy hopes for 'more meaningful' away Ryder Cup win
3 HOURS AGO