Bhullar started with a bogey on the first hole, but on the very next landed an eagle and then proceeded to dominate the course.
The other Indians, too, had a good day with Anirban Lahiri returning three-under 68 to be tied 15th, while Himmat Rai (69) was tied 25th.
Shiv Kapur and Ajeetesh Sandhu, 70 each, were tied 34th, but SSP Chowrasia struggled with a two-over 73 to be in tied 82nd place.
Playing alongside defending champion Chan Yih-Shih (73), Bhullar's eagle on the second was followed by birdies on third and fourth and he added another one on ninth to turn in a healthy four-under 31.
On the back nine, he made no mistakes, had birdies on 12th and 13th and then added two more on 15th and 18th for a superb 63.
Lahiri had three birdies in a row from second to fourth, but bogeys on fourth and sixth set him back. On the back nine, he birdied the 13th and 15th and missed a couple of others to finish at 68.
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Bhullar, who has one win, one second and one ninth-place finish in his last five starts, sank a 35-footer on the second hole and had seven other birdies.
"When you know mentally that you're striking the ball good, it'll be a matter of putting and if you putt well, you will score. Today was one of those 'Super Sunday' putting," said a delighted Bhullar.
"I canned that putt (on two). It changed the whole game plan. I made a lot of close birdies but holed a lot of long putts. (I also) holed two from 40 feet."
Bhullar holds Macau close to his heart as he finished second here three years ago. (MORE)