Jyoti Randhawa carded a one-under 71 while Rashid Khan bounced back to register a two-under 70 in the Mauritius Open.
Shiv Shankar Prasad Chawrasia is the second highest ranked Indian golfer in the world behind Anirban Lahiri.
Rashid Khan shares the fifth spot with Australia's Josh Younger and the experienced Thaworn Wiratchat of Thailand.
Rashid Khan finished tied third at the Mercuries Taiwan Masters, a fortnight ago.
Rashid Khan is two shots behind leader Liang Wen-Chong, who is five-under 211.
The 24-year-old, who won two Asian Tour titles last year, fought back strongly with six birdies against two bogeys for a 70 that gave him a total of six-under 138.
Rashid Khan carded four-under 68 to be second in the first round. Another Indian S. Chikkarangappa tied 12th.
Bhullar had five bogeys against four birdies for his 71. Four of the bogeys came on the front nine, while he had two birdies each on front and back nines. Bhullar has round 72, 70 and 71 for a total of three-over 213 and is tied 42nd, up from overnight 45th.
As the cut fell at three-over 143, only Bhullar (72-70) and Rashid (70-73) survived the midway cut among the eight Indian golfers who started the week.
Apart from Rashid Khan, other Indians like Digvijay Singh, Arjun Atwal, SSP Chawrasia, Jyoti Randhawa and amateur Viraj Madappa were all in danger of missing the cut.