The two Americans started the day tied for the lead but it turned out to be a mismatch as Thompson, five years younger than Wie, displayed more aggression, greater composure and a better touch on the greens.
She sank a series of 10-foot putts to deliver a proverbial knockout by taking a five-shot lead at the turn, an advantage which she never looked remotely in danger of blowing as she cruised to her first major title.
“I’ve worked my whole life to win a major and this was my main goal coming into this year, so I’m excited and so grateful,” Thompson told Golf Channel after carding 68 to finish at 14-under-par 274.
“I drove it pretty well this week but I did make a few good putts so overall a pretty solid week.”
Only Morgan Pressel, who won the 2007 Kraft Nabisco Championship at the age of 18, has won a women’s major at a younger age.
Wie had a golden chance to seize her first major title and justify the media hype that has followed her for more than a decade.
She played conservatively off the tee for the most part, however, and was unimpressive on the greens with her unusual stooped putting style.
Not for the first time, she missed several short putts, including a two-footer at the eighth hole, and her timidity ultimately cost her any chance of winning.
Trailing by four strokes at the 13th hole, she inexplicably left a five-foot birdie chance short, surrendering any faint chance of making it a contest.
“I think I got to a point I tried too hard to make birdies and I was forcing everything,” Wie said after shooting 71 to finish on 11-under.
“If I’d just let it happen, I think I would have rolled a couple more putts in. I wanted to make those putts so badly. At the same time, Lexi played amazing today.”
English teenager Charley Hull started the day two strokes off the lead but a demoralising four-putt double bogey at the eighth ended her chance. She shot 76 to tie for seventh on four-under.
Thompson seemed destined for greatness after qualifying for the US Women’s Open at the age of 12, and winning her first LPGA event at 16.
At the time she was the youngest ever LPGA winner but, as Wie has shown, there are no guarantees that youthful promise will turn into major success.
Thompson has proved no flash in the pan, though, and her power and poise suggest she will be winning tournaments for a long time.
Wie, on the other hand, still has to prove herself on the biggest stages in women’s golf.
(Reporting By Andrew Both in Cary, North Carolina)