Lee carded a final round of 64 to set the clubhouse target of 18 under par and briefly held a two-shot lead when she made a fourth birdie in the last five holes on the 18th.
Lee6 had started the day five shots clear of American teenager Yealimi Noh and made the ideal start with a birdie on the first, but played the next eight holes in five over par to throw the event wide open.
The 25-year-old bravely rallied on the back nine and birdied the 16th, 17th and 18th to force extra holes as Noh, who led by one following her fourth birdie of the day on the 13th, missed from eight feet on the last to join the play-off.
The players returned to the par-five 18th for sudden death and, after both found the fairway off the tee, Lee piled on the pressure with a superb approach to inside 10 feet.
Lee6 mishit her second shot to find the water in front of the green and when she was unable to hole out with her fourth following a penalty drop, the tournament was effectively over in something of an anti-climax.
Lee, whose brother Min Woo won the Scottish Open on the European Tour a fortnight ago, completed the formalities by lipping out for eagle before tapping in for a winning birdie.
Lee, whose seven-shot comeback equalled the largest in a women’s major, told NBC: “I never really thought about it (winning) when I was playing.
“I just tried to make as many birdies as I could, I think I saw the leaderboard maybe once or twice. I just tried to play to the best of my ability and it’s really great to win a major. It’s just really amazing.”
Ireland’s Leona Maguire finished in a tie for sixth on 13 under after earlier equalling the lowest round in major history with a stunning 61.
Maguire birdied her last four holes and carded 10 in total to match the score set by South Korea’s Hyo Joo Kim at the same venue in 2014 and equalled by Lee6 on Friday.
“We saw Lee6 do it the other day and you know it is possible, but everything has to go your way,” Maguire said. “I felt like I have been playing really well the last couple days, I just didn’t hole any putts.
“Birdie on the first and then holed a really nice putt on the second and just kind of snowballed from there. I think I got my fair share and I made two really good pars on 12 and 13, which kept the momentum going, which was nearly as important as some of the birdies.
“I have just been really consistent, giving myself opportunities and my irons have been good. It has really boiled down to how I putt and there really was not a whole a lot of difference between the 61 and 71 yesterday.”
England’s Georgia Hall eagled the 18th in her closing 64 to share sixth with Maguire, Lydia Ko and In Gee Chun.