Australian Steven Bowditch (67), boosted by an eagle at the par-five 16th, finished second on 13-under.
Bae posted four bogeys in a seven-hole stretch mid-round but the 28-year-old held on to take the win and pocket $1.08 million for his second victory on the PGA Tour.
He also has 12 international wins.
Bae built a six-shot lead early in the final round but made the mistake of looking at the leaderboard as a mixture of nerves and excitement got the better of him as he frittered away most of his advantage.
However, none of his closest rivals could launch a serious challenge and Bae had the luxury of missing a series of short putts without ever letting his lead dip below two strokes in demanding, breezy conditions.
"Sometimes I felt excited too much and sometimes nervous, and sometimes lost focus a little," he told reporters.
"I didn't want to look at the scoreboards, but I did. I looked a lot. That's why I made a lot of bogeys on the back nine."
It was Bae's first top-10 finish since he won the Byron Nelson Championship in May of last year, but he expressed confidence that this latest success would be the first of many.
"After the first win, I didn't play well last year," he added. "I was very frustrated, very anxious and nervous, but now I've got the second one, I think third and fourth will come easy since I have the confidence."
Bae said he hoped to earn a spot on the International team for the Presidents Cup to be played in his homeland next year and also wanted to represent South Korea when golf returns to the Olympic programme in 2016.
(Reporting By Andrew Both in Cary, North Carolina; Editing by Peter Rutherford)
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