Lee, 23, who shot a one-under-par 70 to finish on six under, trailed overnight leaders Celine Boutier and Yu Liu by two shots at the start of the day, but their challenge faded in Charleston.
Americans Angel Yin and Lexi Thompson and Korean Ryu So-yeon were tied for second place on four under.
England's Charley Hull and world number one Ko Jin-young finished on level par.
Lee has added the number 6 to her name because she was the sixth player called Jeong-eun Lee on the Korean LGPA.
"That's why they put it down as Jeong-eun Lee6," she said. "But this is my lucky number too, so I would love to put it down as Lee6 as my last name."
She is the 16th player from South Korea to win a major, the most of any country other than the US.