Kuwaki and Esther Henseleit finished regulation at five-under 279 after Henseleit made a long birdie putt on No. 18. Kuwaki then won with a par on the second extra hole at Royal Lytham & St Annes.
The 23-year-old Japanese player closed with a one-under 70 to earn her first major title and $1.5 million. Yealimi Noh finished one stroke behind in third.