Yang shot a final-round 3-under-par 69 to get to 9-under 207 for the tournament but Seo Hee-kyung had a 68 to also get to 9-under, leading to the playoff.
Yang's drive at the par-5 18th on the first playoff hole ended up in the right rough. Even though she had a long third shot, Yang's third ended up 15 feet from the hole. Seo missed her chance for birdie and Yang made hers for the win.
"I have been waiting for this championship for a long time and I'm really happy get it in my home country," Yang said. "I think still I can't believe it."
Seo, who won the LPGA's Kia Classic in March 2010, has lost in LPGA playoffs four times since then.
Yang opened the final round of the 54-hole event one stroke behind Anna Nordqvist and Katherine Hull-Kirk. The leaders tripped early Sunday and Nordqvist shot 3-over 75, which left her tied for eighth at 4-under. Hull-Kirk didn't have a birdie en route to an 8-over 80 and slid all the way to 1-over and a tie for 32nd.
Yang's third round featured a birdie at the eighth hole and a bogey at 11. An eagle at the par-4 15th and a birdie at 18 left her at 9-under.
Seo's round included four birdies, two bogeys and an eagle at No. 11, another par 4.
Michelle Wie fired a bogey-free 6-under 66 and pulled into a tie for third with Kim Sei-young, who shot 69 Sunday, and defending champion Suzann Pettersen, who was 2-under 70 in the final round. They finished at 8-under 208.