The 40-year-old, who was one shot behind the overnight leader, returned to the Emeralda Golf Club course after the long wait and birdied the last for a round of five-under-par 67 and a 72-hole total of 19-under 269.
Juvic Pagunsan (66) of Philippines, Kaname Yokoo (70) of Japan and South Korean Song Young-han (68) finished on 17-under 271, tied for the second place.
"I can't believe it," the long-haired Choi said after clinching the £660,000 tournament in Jakarta, co-sanctioned by OneAsia and the Japan Golf Tour.
"I thought we might not be able to finish. I really didn't want to have to do it all over again tomorrow."
Excessive heat and humidity had forced Choi to pull out of this month's Thailand Open after the first round but he adapted much better to the similar taxing conditions in Jakarta.
"I was better prepared," he said. "This time I had enough towels and ice, and I used an umbrella around the course."
Trailing overnight leader Yokoo by a shot, Choi grabbed the lead with an eagle on the opening hole but came under pressure after dropping a shot on the 15th.
But two successive birdies on the last two holes ensured he picked up the winner's cheque of £118,390.
Reigning Asian Tour Order of Merit winner Thaworn Wiratchant of Thailand finished with a four-under-par 68 for a share of the seventh place.