Kim, who shot a nine-under-par opening round of 61, the lowest ever round in a men or women's major, took a one-shot lead into the final round but the 19-year-old trailed the experienced Webb by one going up the 18th hole.
But the 39-year-old Webb, who was chasing an eighth major title and her first at the Evian Championship, bogeyed the final hole, which gifted Kim the victory after she rolled in a birdie to card a three-under-par 68 and finish in a total of 273.
South Korea's Jang Ha-na and Hur Mi-jung finished tied in third on nine-under, while Norway's defending champion Suzann Pettersen finished sixth, four shots off the lead.
(Writing By Michael Hann, editing by Mark Meadows)
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