Buhai had a five-shot lead going to the final round but a triple bogey on the 15th hole put her level with Chun. Both Buhai and Chun missed long birdies on the 18th and headed into a playoff after finishing 10-under-par in regulation play.
Under pressure, the South African held her nerve and survived three playoff holes against Chun before battling back with a glorious bunker shot on the fourth playoff hole.
Buhai then stroked home her par putt to seal the playoff win, sparking 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 with a lot of grey hairs right now, after that 15th hole!" Buhai said.
"But I was very proud of the way I dug deep to keep myself together and get into the play-off. I was surprisingly calm. I just tried to stay in the moment.
"My caddie said, show them why you're number one in bunkers. Maybe it's something to do with South Africans here in bunkers! It's a good stomping ground for us... For me to be a female South African major winner, I have no words, it's life changing!"
Buhai becomes the second women's major winner from South Africa, joining Sally Little.
