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.
Current Asian Tour Order of Merit leader Anirban Lahiri got five birdies on the fourth, sixth, ninth, 10th and 14th holes against two bogeys on the first and 13th to share the spot with 17 others on Thursday, while Frenchman Gregory Havret fired seven-under 63 to hold a one shot lead against second placed Lasse Jensen of Denmark.
Rashid Khan finished ninth at the Indonesian Masters last year and will face another stern test with the likes of former world number one Lee Westwood of England, Korea's Y.E. Yang and Denmark's Thomas Bjorn expected to draw the crowds to the Royale Jakarta Golf Club.
Rashid Khan has emerged as one of the region's most exciting players and he is getting ready to increase his winning tally at the Malaysian Open February 5-8.
Anirban Lahiri ended the year on a brilliant note by earning a European Tour card for the first time in his career after finishing inside the top-25 of the European Tour Q-School Final Stage.
Arjun Atwal, who has been trying to re-discover his form on the Asian Tour last few weeks, started from the tenth and was one-over after five holes, but then fired four birdies in a row from 15th to 18th.
Rashid Khan and SSP Chowrasia, placed eighth and ninth respectively, along with five-time Asian Tour winner Anirban Lahiri (second) are the three Indians who now feature prominently on the money list as the region's premier Tour heads into its exciting stretch of the season where the battle for the merit crown intensifies.
Rashid Khan's winning cheque of USD 135,000 will also catapult him into the top-10 of the Asian Tour Order of Merit rankings and also get him into the top-200 of world rankings, making him the second highest ranked Indian golfer after Anirban Lahiri.
Rashid, who won his first Asian Tour title on home soil in March, birdied the last two holes to stay in the title mix. He reaped the rewards of working with a mental coach, saying it has helped him stay patient on the course.