Lee sat 39th and nine shots off the lead going into the weekend, but the 24-year-old posted rounds of 68 and 66 to finish six under par at Dundonald Links in North Ayrshire.
Karrie Webb had looked on course for victory when she eagled the 14th for a two-stroke lead, but the Australian bogeyed the 16th and double-bogeyed the 17th to allow Lee to snatch victory.
Webb finished one shot back on five under and joint second along with another South Korean, Hur Mi-jung.
Lee made seven birdies on the final day and watched from the clubhouse as Webb missed the eagle putt she needed to force a play-off on the 18th.
Carly Booth was the highest Scottish finisher, finishing on five-over par after a final round of 73.