The 24-year-old Bhullar is three-under 141 for 36 holes and a good showing over the weekend will boost his rankings further.
The other Indian star in the field, veteran Jeev Milkha Singh carded 71 to be tied for 38th place at one-under 143 in Asia's richest event and lone World Golf Championships in the region.
Louis Oosthuizen carded a new course record score of nine-under 63 and moved into pole position and held a whopping five-shot lead over Adam Scott (68) and Ernie Els (63).
Oosthuizen, winner of the 2010 Open Championship, where he held a five-shot lead after two rounds at St. Andrews, dominated the field at Mission Hills with a course record.
Oosthuizen, runner-up at the Masters this year, however saw the course record being equalled by senior and fellow South African Ernie Els (63). He was 16-under, while Scott and Els were 11-under.
Bhullar had five birdies against a lone bogey on the par-5 15th at the Olazabal course.
"It seems like the game is coming back. Today, I hit the ball so good. It was surprising to miss so many putts. Two more days, hopefully I'll start reading the greens a bit better. I'm looking forward to shooting some low digits," said Bhullar, who won the Venetian Macau Open and Yeangder Tournament Players Championship in Taipei recently.
Bhullar tied 10th in the co-sanctioned Asian Tour and PGA Tour event in Malaysia last week, went straight to the practice putting green to work on his lines on the "paspalum" greens.
"This kind of grass, we hardly play on them throughout the season. I guess the more you play on them this week, the better you become. That's the goal setting for me," he said. (MORE)
