Carding 68, Himmat, who missed nine straight cuts from April to September, is now at 11-under 205 and just two shots behind the leader, China's Liang Wen-chong (67).
Himmat is now tied for fourth alongside overnight leader Jazz Janewattananond (72).
Another Indian in sight of a good placing is and a possible shot at the title is SSP Chowrasia (69), who finished tied second last week at Hero Indian Open.
Digvijay Singh (74), Jyoti Randhawa (71) and Abhinav Lohan (71) are all tied for 36th place at four-under 212, while Sujjan Singh (73) dropped to tied 48th.
Himmat had five birdies, two of them in first three holes and another three on back nine. His sole bogey of the day came on ninth. Chowrasia opened with a string of seven pars before he birdied the eighth and bogeyed the ninth.
Three birdies on 12th, 15th and 16th rounded off a fine four-under 68 for Chowrasia, whose last Asian Tour win came in 2011.