Himmat, who has rounds of 69-66-68 is now tied fourth at 10-under 203 and just three behind the leader, Chinese Taipei's Lin Wen-tang (68).
In between Spaniard Sergio Garcia (68) and Shaun Norris (65) of South Africa were two behind at 11-under 202. Himmat is tied with Thaworn Wiratchant (68) at 10-under 203.
Among the other Indians, who made the cut after the third round were Jeev Milkha Singh (68), who moved up from 60th to Tied 29th at two-under, Gaganjeet Bhullar (73), who was 34th, down from 18th at one-under 212. Rahil Gangjee (71) also made the cut at even par 213 in tied 48th and Khalin Joshi (76) squeezed inside despite a ragged 76.
I played really good and to my strategy. It is about sticking to the routine and doing it over and over again. It was good how I bounced back from the double bogey. During the round, I didn't even remember I made a double bogey. For the whole day, I was trying to hit it one shot at a time," said Himmat.
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On the double bogey he suffered on par-3 fourth hole, he said: "I had a nice lie and didn't have a good chip. From there the chip was even harder because it was uphill. A win is what we are all here for. For me it is strictly about playing one shot at a time and enjoying the moment."
World number 12 Garcia endured a topsy-turvy day as well en route to a 68 which kept him in the chase for a first title of the year alongside Norris, who charged into contention with a 65 in Vietnam's richest sporting event.
Thai veteran star Thaworn Wiratchant, bidding for a record 19th Asian Tour victory, carded a 68 to lie three back alongside a resurgent Rai, who also carded a 68. American Paul Peterson (68) will start the final round four shots back of the leader.