The Indian golfer followed up a sedate start with a fine back nine that included two successive chip-ins for a birdie and an eagle to emerge as the best Indian.
S Chikkarangappa (72) was tied 12th but the other Indians were headed to over-par scores.
Malaysia's Danny Chia took advantage of the favourable scoring conditions in the morning to seize the clubhouse lead with an opening five-under 67.
The conditions were excellent for scoring in the morning and then became tougher in the afternoon.
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Rashid, winner of two Asian Tour titles, had eight straight pars before making a birdie on the 18th to turn in one-under after starting from the tenth tee. He added another shot on the par-three second after missing a hole-in-one by six inches. A bogey on third was his first error of the day when he missed an up-and-down for par.
"I played superb on my back nine, which is the front nine. I almost made a hole-in-one on the par-three second hole. I hit an eight-iron to about six-inches short of the cup. I missed an up-and-down and bogeyed the next hole but I managed to recover strongly on the fifth.
"I hit it left and the ball went OB but I was lucky as I managed to find the ball inside the trees. I had a really tough shot there but I hit it 10 yards short of the green and chip in for birdie," said Rashid.