The 24-year-old, who won two Asian Tour titles last year, fought back strongly with six birdies against two bogeys for a 70 that gave him a total of six-under 138.
Rashid was one shot ahead of overnight leader Danny Chia, whose second round 72 gave him a total of 139 but allowed the Indian, who was one behind after first round, to move one ahead after the second round.
Also making the cut were Chiragh Kumar (77-71) and S Chikkrangrappa (72-76) and Himmat Rai (73-75), all in tied-26th.
However, with only Top-50 and ties making the cut, Rahil Gangjee (76-75) and Arjun Atwal (76-75) missed the cut by one. Also making an early exit were Gaganjeet Bhullar (76-78) and Angad Cheema (81-82) as did Daniel Chopra (75-79).
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Rashid, who has had a very modest season with Tied-24th at Hero Indian Open as his best this year, had a rattling double bogey start.
Thereafter, he did not look back.
"I had three straight birdies starting from the fifth which got my game going. I chipped in from greenside bunker on the fifth and made up and down there. I told my caddy if I can shoot three or four-under par, it will be good. But I three-putted on the ninth again. I kept the ball in play on the back nine, made another three birdies although I three-putted on 17th. I holed a six-footer putt for birdie on the 18th, which was a good finish to the round.