Shin was the only player to finish under par at the par-72, 6,600-yard layout, despite an up-and-down final round of one-over 73. Her dominant win was aided in large part by her course-record 64 in the second round, which featured six birdies and an eagle.
She now has 10 career LPGA victories.
Shin said afterward she was "surprised" that she was able to go so low in such difficult conditions.
"I said yesterday, my goal was (to shoot) one-under par every single day. So my goal was four-under," she told the post-tournament press conference. "Because (this is a) really tough course here, when I finished it today, I'm just like, wow, I can (post) good scores on any, any other course, I'm pretty sure of that."
The Women's British Open was the fourth and the final major on the LPGA Tour this season. South Koreans won three of those four big tournaments, with Yoo Sun-young taking the Kraft Nabisco Championship in April and Choi Na-yeon claiming the U.S. Women's Open in July.
Feng Shanshan of China was the other major champion, as the winner of the Wegnmans LPGA Championship in June. For the first time in the tour history, all four majors in a season went to Asians.
Shin has now won two straight LPGA tournaments in the past seven days, after going nearly two years without a victory. She defeated Paula Creamer on the ninth playoff hole to win the Kingsmill Championship last Monday in Virginia.
Golfers were forced to play 36 holes on Sunday after the second round play was postponed to Saturday because of strong gusts. The fourth round was also briefly suspended, with Shin on the 11th tee.
The champion said she was glad to end this tournament on time.
"I'm happy to finish today because I didn't want to play until Monday," she said. "It was a really, really tough and long day, because I played 36 holes with rain and wind. I tried to keep focusing on each shot. So I feel a little tired now."
Shin held a three-shot lead over Karrie Webb of Australia to start the final round at 10-under, after shooting 71 with five birdies and four bogeys in the third round.
The South Korean stumbled with a triple bogey on the first hole in the fourth round, as the wind picked up its speed. She settled down with pars on the next four holes, and her lead actually increased as Webb committed a double bogey, bogey and bogey on her first three holes of the day.
The rout was on as Shin birdied the sixth and the seventh to reach 9-under, while Webb fell further back with a bogey on the sixth hole. Shin picked up three more birdies on the back nine and Webb faltered with two more double bogeys over her final five holes.
The victory here completed a career turnaround for the former No. 1-ranked player who struggled with injuries in recent years.
Shin won the British Women's Open and two other LPGA tournaments in 2008 as a non-member, and added three more victories in 2009 as a tour rookie. She easily won the Rookie of the Year points race and became the youngest-ever money winner in the tour history.
Shin won twice in 2010, including at the Evian Masters in France, a prestigious event that will become the tour's fifth major next season.
The following season, however, Shin developed back pains while attempting to change her swing and was forced to miss about a month of action. She ended the year without a victory. Then in May this year, she underwent surgery on her left wrist.
In the process, she dropped out of the top 10 in the world rankings. Shin climbed to No. 10 after the Kingsmill victory, and is likely to move up further on the strength of the British win.
Park In-bee made a late charge and closed with two birdies on the final three holes for sole possession of second place. It was her ninth consecutive top-10 finish on the tour.
No player broke par in the final round and 13 of 57 players made the cut shot in the 80s over their last 18 holes.
Yani Tseng, the two-time defending champion, went 76-79 on the weekend to finish at 11-over par, tied for 26th. South Korea's Kim In-kyung and Chella Choi tied for 10th at 7-over. (Yonhap News)