The Indian golfer was the best placed Asian in the world-class field. And with one more round to go, Bhullar at 12-under is six shots behind co-leaders Lee Westwood (61) and Louis Oosthuizen (70), who are at 18-under 198.
Bhullar, 24, who has won twice on the Asian Tour in the past two months, fired nine birdies in a flawless round.
The only players to shoot better than Bhullar's 63, were American Brand Snedeker, who shot a spectacular 60 after narrowly missing out on a magical 59 with a missed birdie chance on 18 and England's Lee Westwood (61) who went on to grab a share of the third round lead with halfway leader Louis Oosthuizen, who shot a 70.
Bhullar's senior, Jeev Milkha Singh carded a 73 for tied 46th position on 216.
Four-time Major champion, Phil Mickelson shot a 66 to trail by three strokes in third place as he kept up his bid for an unprecedented third HSBC Champions title.
Bhullar has maintained his impressive form through the season. A week after finishing top-10 at the co-sanctioned Asian Tour and PGA Tour event in Malaysia, he has put himself in position for another terrific showing.
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"It was a smooth 63. Trust me, it was a great round. I had 16 greens in regulation, nine birdies, nine pars. We kind of expect this kind of round when you play good. It's been a long time I've shot low 60. I came here with a lot of positivity in my game. Hit the ball really well and I made nine birdies and nine pars, probably the best I've ever done in my life," said Bhullar.
"You know, I have shot 62 once in an Asian Tour tournament but to shoot a low number in such a big tournament, it means a lot. It will definitely help me in my future tournaments," he added. (MORE)