She also finished with a tournament record of 20-under par.
Hur's last LPGA victory came at the 2014 LPGA Classic, having won her maiden title five years before in the Safeway Classic.
Overnight leader Moriya Jutanugarn (71) and US Women's Open champion Jeongeun Lee6 (70) tied for second place on 16-under.
The tournament ended a three-week LPGA stretch in Europe.
"Gary was very good on Thursday when I bogeyed two holes in a row, he kept telling me I could win", she said.
Lee6, a newcomer to links golf, won the U.S. Women's Open in June in SC.
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Mi Hyang Lee, the 2017 victor, was fourth at 12 under after a 68. "I had a really short third shot, left the putt really short but then rolled in the next one from 30 feet".
"That was raining like today but also a wind blowing 25 to 30 miles per hour", she said.
"I think because she felt like she never played good on a links course, so that's why she kind of pretty surprised what she had done".
Carly Booth, the 2012 victor, finished joint ninth after closing with a 71 for 274.
Low round of the day belonged to Australian 23-year-old Minjee Lee, who went bogey free in a round of 64 (-7). "I was really steady tee-to-green all weekend".
"I imagine there will be a lot of support - I've been over here quite a lot and actually played "Royal" Alyth last Monday", she joked.