Kapur, who became a father for the first time last month, recovered from back-to-back bogeys and fired five birdies on the back nine to take his two-day total to five-under 135 to be the best Indian in the fray.
SSP Chawrasia (70) and Rahul Gangjee (71) brought home improved cards on the second day to total 143 and 144, while S Chikkarangappa scored a second successive 73 to total 146.
Rashid Khan was three-under at the 14th hole in the unfinished second round.
"I almost didn't tee up today. I had a really bad flu last night and was running a temperature. I came back to the golf course at night to see the doctor. I was pumping myself with paracetamols and somehow, I managed to get through today. I guess I was lucky," he said.
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"I putted quite well today, to be honest. I thought my body would struggle to swing but I actually swung the club really well today and hit the ball great. I made a couple of three-putts on the front nine but I came back really good on the back nine with four birdies."
Thongchai Jaidee (66), Fabrizio Zianotti (65) and Todd Sinnott (66) were at tied third spot with a total of 131.
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