The American, 24, had twice been a runner-up at one of the four majors, including at this season's Kraft Nabisco Championship.
But Wie ended her relatively long wait to seal the breakthrough, having turned professional prior to her 16th birthday.
Wie carded an even-par 70 to hold off the fast-finishing Stacy Lewis, as the world number one shot a blistering four-under 66 to finish at even par overall - two shots behind the winner.
Northern Ireland's Stephanie Meadow (69) finished at one over in outright third, ahead of South Korean trio Amy Yang (fourth, 74), Meena Lee (68) and Ryu So Yeon (70) tied for fifth.
Thailand's Pornanong Phatlum, Japan's Sakura Yokomine and American Lexi Thompson were tied for seventh on four over.
Rounding out the top 10 were Scotland's Catriona Matthew, Jenny Shin of South Korea and Canada's Brooke Henderson at five over.