Randhawa, who teed up in Japan three weeks ago for his first event since mid-December, added a one-under 71 to his rounds of 73-75 to get a total of three-over 219.
Meanwhile, Rashid Khan continued to ride his own rollercoaster as he bounced back from a crippling second round of nine-over 81 to record two-under 70 on the third day to share the 14th spot with Randhawa.
Siddikur Rahman, who for the last year or so has been playing with an injured back even as he tried to find ways to get better, found himself leading an European Tour event for the first time as he played very steady golf in the face of very windy conditions.
Also making good upward moves were Rahil Gangjee, from 57th to 25th, as he carded one-under 71, while Arjun Atwal, another one at 57th moved to Tied-41st.
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However, Chiragh Kumar (77), Himmat Rai (79) and Jeev Milkha Singh (80) moved backwards to Tied-48th, Tied-58th and Tied-65th.
For Rashid, it has been a massive up and down over last three days, as he began the week with a superb four-under 68 only to bring in a card of 81 on Friday.
Randhawa, who missed the cut in Japan last month, because of lack of tournament play, looked happy to play only his second event in five months.
Chawrasia said, "I have been playing well and I love
coming to Samui, it's a lovely place and this week was free, so I decide to play here. I also love the course here."
Former Asian Tour number one Liang Wen-chong of China will be gunning for a winning debut at the Queen's Cup to revive his hopes of qualifying for the Olympic Games. The Chinese star was bumped out of the race to Rio de Janeiro following countryman Wu Ashun's victory in Austria over the weekend but he has vowed to keep fighting starting with this week's Asian Tour stop.
Other top stars in the field include title holder Prayad Marksaeng of Thailand, big-hitting Aussie star Scott Hend, Korea's rising star Jeunghun Wang and Bangladeshi Siddikur Rahman.
Straight-shooting Siddikur is happy to return to his happy hunting ground where in six previous appearances at the Queen's Cup, he has finished top-three on three occasions and not finished lower than 16th place.
The 31-year-old is also keen to atone for the disappointment of losing to Wang at the AfrAsia Bank Mauritius Open last month where he led by three shots with three holes remaining.