Kuwaki and Henseleit finished regulation play tied at five under par after the German holed a lengthy birdie putt on the 18th to force extra holes.
American Yealimi Noh, who had held the overnight lead and started the day strongly, finished third at four under.
Kuwaki sealed victory on the second playoff hole, after Henseleit missed her par attempt and tapped in for bogey, becoming the second Japanese champion of the tournament in succession, after Miyu Yamashita.
After beginning the day among the chasing pack, Kuwaki steadily climbed into contention as Noh began to feel the pressure. She moved into a share of the lead with a birdie at the 13th and stayed patient over the closing stretch before posting the clubhouse target at five under.
Noh looked set to control the final round but a pair of bogeys at the seventh and eighth cut her advantage. She briefly recovered, regaining a share of the lead with a birdie at the par-four 13th, before another dropped shot at the 14th left her trailing Kuwaki by one.
Henseleit also produced a strong back-nine charge. After slipping back with bogeys at the eighth and ninth, she birdied the 11th, 12th and 15th to draw level with Kuwaki, only to drop a shot at the 16th. The German refused to relent, however, rolling in a crucial birdie putt at the last to force the playoff.
World number one Nelly Korda briefly held the clubhouse lead after a closing three-under 68 but it was not enough to challenge for the title, leaving her tied for fourth on two under with world number two Jeeno Thitikul.
South Korea's Haeran Ryu saw her bid for a third consecutive major fade with bogeys at the 17th and 18th, finishing tied for sixth on one under alongside home hopes Lottie Woad and Charley Hull.