The American, tipped for stardom even before she turned pro at the age of
15 in 2005, finished with a two-under total of 278, two strokes in front of world number one Stacy Lewis, who kept the pressure on with a final-round 66 for 280.
"I just had a lot of fun out there," said Wie. "I woke up so excited. I was so grateful for this opportunity."
Wie saw a three-stroke lead shrink to one with a double-bogey at 16. But she responded by burying a 25-foot birdie putt at 17 to take a two-stroke lead to the final hole.
"I got a lot of goosebumps walking up 18," said Wie, who allowed herself a small smile and wave as she was greeted at the 18th green by a standing ovation.
Wie, swept along by a wave of hype and endorsements when she turned pro, drew criticism for her early insistence on trying to challenge in men's events before she'd become a proven winner against the world's top women.
Sunday's triumph was her fourth on the LPGA Tour, and her second of the year.
In April she won the Lotte Championship in her home state of Hawaii to end a victory drought stretching back to 2010.
The major title, on the course where Germany's Martin Kaymer lifted the US Open trophy in the second men's major of the season a week earlier, also helped erase the memory of her near-miss in the Kraft Nabisco Championship this year.
She went into the final round of the year's first major at Rancho Mirage tied for the lead but ended up second behind 19-year-old Lexi Thompson.
"Obviously there are moments of doubt," Wie said when asked if she ever wondered if she could win on the game's biggest stages.
"But at the same time I just had so many people around me ... they never lost faith in me. That's what kind of pushed me forward."
Lewis, who started the day six shots off the lead shared by Wie and South Korea's Amy Yang, posted an impressive eight birdies in her four-under 66.
That included a birdie-birdie finish that had her three shots behind Wie as she walked off the course.
"It feels great to finish the way I did," Lewis said. "I knew I needed to go out early today and post a number and make Michelle earn it."
Northern Ireland's Stephanie Meadow, playing her first tournament as a professional, carded a one-under 69 to finish third on one-over 281.
Yang struggled to a four-over 74 that put her alone in fourth on 282.