Atwal (71) slipped from sixth to T-10, while Bhullar moved up marginally from T-12 to T-10 with a card of 69.
Among other Indians, Ajeetesh Sandhu (70) ended Tied- 21st, while Rashid Khan (71) was T-48th and Shiv Kapur (74) and Jyoti Randhawa (75) were T-57th.
Bhullar had four birdie against one bogey while Atwal had two birdies and two bogeys.
Peterson dropped two bogeys in his closing four holes, but still ensured victory with a birdie on 18 to sign off with a five-under-par 66.
More From This Section
Petersons lead was briefly threatened when he dropped two shots on 15 and 17 but the American maintained his composure by sinking a crucial birdie at the last hole for his Asian Tour breakthrough.
Japans Satoshi Kodaira set the course record at the Pun Hlaing Golf Club with a stunning 63. However his final day heroics were not enough to overtake Peterson, leaving him to settle for a share of second place with compatriot Tomoyo Ikemura.