With the victory, Wie claimed her fifth career LPGA title with a final-round seven-under 65, for a closing score of 17-under par 271.
Kim Sei-young briefly threatened to shoot an LPGA-record matching 59 but a bogey on the 16th stalled her progress and the Korean had to settle for a course record 10-under 62 to finish in a tie for 10th on 12 under.
She had earlier just missed several birdie opportunities, but a victory was always unlikely, and the double bogey dropped her back into a share of tenth.
Shin, in the group ahead of Wie, had stormed into the lead with eight birdies in 11 holes and she reached the 18th with a one-shot lead, but an errant approach and duffed chip led to her first bogey of the day and opened the door for Wie.
Wie had been winless since her maiden major victory at the 2014 U.S. Women's Open, and it was clear how much the victory meant to her.
Their playing partner Brooke Henderson finished with a birdie to card 68 and move into the tie for second, which also included Shin after her final round of 65. "It's been a tough journey but I'm just really proud that I pulled myself out of it".More news: Livescore: Latest Barcelona vs Atletico Madrid result (Week 27), 2017/2018 LaLiga scores
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Wie was entrenched in a four-way tie for the lead as she watched her approach shot land short of the green, but just moments later she was galloping towards the hole and pumping her fist as her ambitious 45ft effort found the cup.
American Nelly Korda, whose older sister Jessica won last week's event in Thailand in remarkable circumstances, fired the equal best round of the day to grab the outright lead at 15-under. Overnight leader Nelly Korda had a nine-footer on the 18th green to force a play-off but it didn't drop.
Korda admitted to feeling a little sibling heat coming in to the Sentosa Golf Club, saying she had been reminded that it was her turn to win "all the time".
But she still faced an anxious wait before being declared the champion.
"I had nine putts on the back nine, which is really awesome", Henderson said. "I felt like I had a good year last year, a year where I built confidence, and I just want to keep building confidence from there". "I wasn't really thinking about whether I was going to be in the lead tomorrow or chasing, but Nelly had a really solid game today", Kang said. I called him in, I was like, "Yo, Matt, you've got to help me read this putt".
Throughout her career, Wie has played under tremendous pressure, all of the expectations that come with being a prodigy have been following since she turned professional in 2005. I think it's been kind of well documented.