Poulter (70) bogeyed the 16th and 18th holes to blow his lead. American Anthony Kim (71) tied for third with South Korean Kim Wi-joong (72).
The 22-year-old Bae totaled 11-under 273 at the Woo Jeong Country Club and won $240,000 to climb to fifth on the Asian Tours Order of Merit. Its his second victory on the tour.
He birdied the 10th hole and made par on each of the final eight holes.
That birdie gave me the confidence needed to keep it going in the closing holes, Bae said.
Poulter finished runner-up at the British Open this year.
I came here to win but I am going home second, so Im not very happy, Poulter said. But its nice to come here with so many fans, and Im glad I could show them some good golf this week.
Kim, who helped the U.S. team win the Ryder Cup, was eager to win in his ancestral home.
I am very disappointed, he said. I let a lot of shots go today and this week. There is a lot for me to learn, but hats off to the winner who played great.