Bhullar, who was going great guns at four-under after 12 holes, suddenly plummeted to one-under by the end. Bhullar is now four-under for 36 holes with rounds of 69 and 71.
The sole representative from India at the WGC-HSBC is now eight shots behind the leader Dustin Johnson, who carded a record nine-under 63 to get to 12-under 132.
"It's hard to explain what went wrong there but I'm sure I'll be back with a clear focus tomorrow," said Bhullar, who signed for a two-day total of four-under-par 140, eight shots back of American Dustin Johnson, who equalled the course record with a 63.
The 25-year-old, ranked third on the Asian Tour Order of Merit, started his round four shots back of overnight leader Rory McIlroy of Northern Ireland.
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After four straight pars from the 10th, Bhullar stepped up a gear with a birdie on the par-five 14th. He birdied again on the 16th before reaching the turn in 34. Two birdies in his next three holes saw the Indian trail the leaders then by a single shot. He parred the next three holes before the disastrous streak from the par-four seventh to the ninth.
Major winner Bubba Watson and fellow American Boo Weekley shared second place with world number six Rory McIlroy of Northern Ireland after the trio returned with matching seven-under-par 137. Ernie Els of South Africa is among the six players bunched in tied-fifth on 138.
China's Liang Wen-chong and Korea's Jin Jeong finished as the highest-placed Asians after carding rounds of 67 and 69, respectively.