Janangelo and Bastel (72) ended the event at 4-over-par 217. Janangelo won the title on the third extra hole at Leawood South Country Club.
The 23-year-old Janangelo, who was a four-time All-American at Duke, won for the second time this season and moved to the top of the money list. She is less than $2,000 ahead of Bastel as both have played all seven events this year.
Janangelo won despite not posting a birdie in the final round. She had three bogeys and a double-bogey in her round of 76.
Bastel was 3-over for the front nine with a birdie and four bogeys. On the back nine, she made a charge with a bogey and three birdies to force the playoff.
Kim Augusta, Vikki Laing, Allison Fouch and Rachel Bailey shared third at 7-over-par 220. Brandi Jackson was one stroke further back at plus-8.
Ji Min Jeong and Nontaya Srisawang tied for eighth at 9-over-par 222.