The 24-year-old had built a six-stroke advantage heading into the final round, which she saw dwindle to two at one point Sunday.
But she overcame numerous obstacles -- such as hitting the hazard next to the 10th fairway -- making several key shots down the stretch and ultimately finishing four shots ahead of second-place Amy Yang at 7-under 281.
The Korean had racked up five previous LPGA Tour titles, but collected her first major after several near-misses.
Yang fired a 1-under 71 to end at minus-3 -- the only other player to finish below par.
Claiming third was Sandra Gal (74) at 1-over 289.
Swim Week Miami Beach 2014 [PHOTOS]