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.
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.
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