She was the only player to finish under par for the tournament, ending on nine-under 279 to complete an Asian sweep of the year's four women's Majors.
Compatriot Park Inbee birdied the 18th hole to take second place on level par for her four rounds.
American Paula Creamer fired a fourth-round 72, the joint-best round of a difficult final day, to take third.
Australian seven-times major champion Karrie Webb's title challenge evaporated during her final round 82 as conditions wreaked havoc with scorecards.
The weather had been a problem all week, gusts of up to 60 miles per hour on Friday leading to a suspension of play which forced players to complete their third rounds on Sunday before a quick turnaround.
Creamer praised Jiyai's performance in the wind.
"It is so hard out there. It just shows what Jiyai is doing. That's pretty good golf out there," she told the BBC.
"I think we should all pat ourselves on the back."
Koreans Yoo Sun-young and Choi Na-yeon won the Kraft Nabisco and women's U.S. Open titles this year and China's Shanshan Feng took the LPGA Championship.
- Karrie Webb