Gleeson was three shots of the pace after the second round but peppered the flags with accurate iron shots for a three-day total of 16-under-par 200 at the Delhi Golf Club to hold a one shot lead over Chiragh Kumar of India.
Overnight leader Kumar rued a cold putter as he posted a 70 while Lu Wei-chih of Chinese Taipei, winner of the Yeangder TPC last week and Scotland's Ross Bain were a further four shots back on 205 in the US$1.25 million Asian Tour event.
Gleeson got off to a fast start with two opening birdies before turning in 34. He sparked into life in his homeward nine with five birdies against one bogey where his approach shot flew over the 18th green and into the greenside bunker.
"It is the third day and always a tough day to find the right frame of mind. Chiragh and I both had flying starts which were great but I'm happy I hit my approach shots close to the holes," said Gleeson.
The Chinese Taipei based Australian has been enjoying a rich vein of form since finishing second at the Macau Open last month but he is not taking his lead for granted.
"This course is so difficult. I'm so nervous on every hole to be thinking about anything else. I still got a lot of work to do out there," said the two-time Asian Tour winner, whose last victory dates back to 2008.
Kumar, a 2006 Asian Games team silver medallist, turned in 34 highlighted by three birdies against one bogey but failed to convert his birdie chances on the back nine where he made nine consecutive pars.
"I just didn't read my putts as well as I did in the first two rounds. You can't read them perfectly every day. It was just one of those days," said Kumar, who is searching for a maiden Asian Tour victory.
Chinese Taipei's Lu put himself in good position of securing back-to-back victories after charging up the leader board with a 12-yard chip-in birdie on seven for a 66.
"My putting could have been better but I won't complain with my score. I'm really confident after my win last week and will do my best to narrow the gap on David," said Lu.
Bain, who is also in the hunt for a first Asian Tour victory, eagled the first hole for the second consecutive day courtesy of a monster 70 feet putt for a 68 to lie five shots off the lead.
"I hit a ridiculous putt on the first hole again and that was a bonus. It is those sort of things that happen that nullified some other putts I didn't hole for birdies. All in all I really played well and my game is in good shape," said the 35-year-old, who finished second in the 2001 Indian Open.
Leading third round scores
200 - David GLEESON (AUS) 68-66-66.
201 - Chiragh KUMAR (IND) 64-67-70.
205 - LU Wei-chih (TPE) 71-68-66, Ross BAIN (SCO) 65-72-68.
207 - S.S.P. CHOWRASIA (IND) 69-70-68, Adilson DA SILVA (BRA) 68-71-68, Daisuke KATAOKA (JPN) 72-66-69, Chapchai NIRAT (THA) 69-67-71.
208 - LAM Chih Bing (SIN) 70-71-67, Himmat RAI (IND) 69-70-69.
209 - Marcus BOTH (AUS) 71-73-65, Boonchu RUANGKIT (THA) 70-73-66, SIDDIKUR (BAN) 70-70-69, Zaw MOE (MYN) 65-74-70, Harendra GUPTA (IND) 72-66-71, Scott BARR (AUS) 67-70-72.
210 - Gaurav Pratap SINGH (IND) 72-72-66.
211 - Edoardo MOLINARI (ITA) 71-70-70