Bugai had a five-shot lead going into the final round, but a triple bogey on the 15th hole put her level with Chun. Both Bugai and Chun missed long birdies on the 18th and headed into a playoff after going 10 under par in the main event.
Under pressure, the South African held her nerve and survived three play-off holes against Chun before hitting back with a superb bunker shot on the fourth play-off hole.
Bugai then stroked her par putt to seal the playoff victory, prompting a celebration from her husband, while Chun had to settle for second after a bogey.
“I know there are a lot of people in South Africa right now with a lot of gray hair after the 15th hole!” Bugai said.
“But I was very proud of the way I did my best to hold my own and make the playoffs. I was surprisingly calm. I just tried to stay in the moment.
“My caddy said show them why you’re number one in the bunkers. Maybe it has something to do with the South Africans here in the bunkers! It’s a good venue for us… For me to be the women’s winner in South Africa, I’m speechless, it’s life-changing!”
Bugai becomes the second winner of a women’s major from South Africa, joining Sally Little.
(Reporting by Manasi Pathak in Bangalore)