Backing up his impressive 67 on day two, the 43-year-old carded a third-round 68 at the Greg Norman-designed Al Mouj Golf for a seven-under-par total, sitting five shots behind three joint-leaders in a share of ninth position.
On a tightly-bunched leaderboard, Englishman Matthew Southgate (69) shares top spot with Joost Luiten of the Netherlands and Frenchman Julien Guerrier after they stepped up their title bids with matching 66s.
Another Englishman, Chris Wood, sits a shot behind, closely followed by Spaniard Adrian Otaegui, but Gallacher will have the leaders in his sights if he can produce more of the same over the closing 18 holes in the £1.5 million event.
The two-time Dubai Desert Classic winner has now gone 38 holes without dropping a shot - a notable achievement on a course where most players have suffered fluctuating fortunes this week - since running up a quadruple-bogey 8 at the 16th in the opening round.
Gallacher, who is on course for his best finish since tying for 12th in last October’s Dunhill Links Championship and first top 10 in more than a year, birdied third of the par 5s - the third, seventh and 12th - in the third round before completing another good day’s work by making his fourth gain at the 17th, a tricky par-4.
David Drysdale (70) and Connor Syme (72) sit on four-under and three-under respectively, with Paul Lawrie (72) on level-par, but Marc Warren (80) and Bradley Neil (79) slipped to five-over and six-over after disappointing days.
In his first outing since withdrawing in Dubai due to back trouble, Drysdale continued to give a good account of himself, though a double-bogey at the 13th undid some of his good work earlier as he covered the first 12 holes in four-under.
Syme, who would have been pleased to make it to the weekend for the first time since winning his European Tour card, was three-under for his round before running up a double-bogey 6 at the ninth then coming home in one-over.
Lawrie, who will be looking forward to next week’s Qatar Masters after winning that event twice in the past, dropped three shots late on as he struggled on the greens for the second day running.
In a repeat of the tough day he endured in the final round of the Maybank Championship in Malaysia a fortnight ago, Warren had a triple-bogey and double-bogey as he was out in 44 before reeling off nine straight pars on the back nine.
Neil, who won his European Tour card on this course in November, had been on a high after he covered his last eight holes in a brilliant seven-under in the second round to make the cut.
But the 22-year-old could only muster one birdie - at the seventh - and saw two par 3s cost him five shots as the Blairgowrie man’s learning curve continued.
Elsewhere, Aberdonian Michele Thomson and Melrose-born Karis Davidson were unable to sustain fast starts in the third round of the ISPS Handa Australian Women’s Open in Adelaide.
Starting her round at one-over for the tournament, Thomson was three-under for the day at the turn before coming home in four-over at Kooyonga Golf Club, where the bulk of the damage being done by a double-bogey at the 17th.
“The back nine wasn’t very good,” she admitted aftrerwards. “There were a few mistakes that probably shouldn’t have been in there, but I can take the positives from the front nine and hopefully do the same again tomorrow.”
Even overnight, Davidson birdied her opening three holes to move in to a tie for eighth but five dropped shots in four holes to close out the front nine proved costly.
The 19-year-old, who now calls Queensland home, also finished at two-over, leaving her and Thomson tied for 50th.
“I had a good back nine with all pars but it was three really simple bogeys and the ninth was just a real bad hole,” said Davidson, who finished second in the recent Oates Vic Open in her first Tour event as a professional.
“I’m hitting the ball well, I just need to not do that again. I’ve been really enjoying it as well and I think that’s the main thing.”
On 11-under, Korea’s Jin Young Ko leads by four shots from home player Hannah Green, with two other Koreans - Hyejin Choi and Sun Young Yoo - a further shot back in joint-third.
Shot of the third day came from Swede Jenny Haglund, who won a Genesis sports car for a hole-in-one at the 14th.
“I’ve made a couple of holes-in-one before, but this is obviously the biggest and most important for me - it’s fantastic,” said Haglund.
In South Africa, Jack Doherty is sitting in the top 20 heading into the final round of the Sunshone Tour’s Dimension Data Pro-Am at Fancourt.
In an event won last year by Paul Lawrie, Doherty shot a third-round 68 on the Links Course for an eight-under-par 209 total.
Three home players - Tjaart van der Walt, Vaughn Groenewald and Breyten Meyer - share the lead on 14-under, two ahead of another South African, Jaco Ahlers.
Former winner Alan McLean and fellow Scot Doug McGuian are joint-43rd on four-under, two better than Jack McDonald.