He now shares the lead with Louis De Jager of South Africa, who produced a bogeyfree 67.
Still recovering from a 16-hour journey from Kuala Lumpur, Atwal is searching for a ninth Asian Tour title and his first since 2014.
Atwal, a former Asian Tour number one and captain of the Asian team for next month's EurAsia Cup, enjoyed a solid front nine 32 before adding his fifth birdie on hole 14. He was ahead by one-shot heading into 18 but missed a four-foot par putt to finish on 13-under-par 200 at the Heritage Golf Club.
"I played solid all day except for a blip on the last hole which won't bother me. It did play harder today. It was definitely blowing harder out of the three days," Atwal said.
More From This Section
Talented Filipino Miguel Tabuena birdied the closing two holes to stay one-shot behind the leaders following a round of 67. He shared the third place with South Africa's Dylan Frittelli, who also birdied the last hole for a 68.
De Jager, who said he is inspired to win the tournament after playing in a pro-am with South African legend Gary Player last week, is playing the lead group for the first time in a tri-sanctioned event.