Tied after the scheduled 36 holes, Shin was conceded victory at the par-4 first by her 16-year-old opponent, ending the final match of the six-day tournament.
Shin became the youngest champion since Aree Song, who was 13 years, three months and seven days old when she won in 1999.
After being behind by as much as 3-down, Shin won the 36th hole with a par to force extra holes. Hurst then knocked her approach at No. 1 into the water, took a penalty, found a bunker with her next shot and conceded the hole and the match.
'She gave me a little present,' said Shin, who was on the green in two when the match was conceded. 'After I got the trophy I was like, 'Is this mine?''
Hurst was competing for the championship just three months following the death of her father, Joe, in April, and one month after playing in the U.S. Women's Open last month.
She three-putted for a bogey at the 36th hole -- Carmel Country Club's 495- yard, par-5 18th -- from just 25 feet away.
'It's really disappointing, to three-putt the last hole and all,' said Hurst, of Melbourne, Florida.
The match was all square following the first 18 holes and remained even through the next three. Hurst then took a 3-up lead by winning the next three holes with two birdies and a par at the sixth.
Shin rallied after the turn, though, and trimmed her deficit to 1-down with a par at the 10th and 13th holes. Hurst briefly went 2-up after parring the 14th, but was only 1-up again following a bogey at the 15th.
In the first 18 holes, Shin made birdie at the par-4 third to take the lead. She moved 2-up several times, including at the 11th hole, where she rolled in a 36-foot birdie putt.
But Shin began struggling to hit greens, and Hurst squared the match with pars at the 12th and 14th holes. Hurst took the lead briefly with an 8-foot par putt at the 16th, then coughed it up when she missed a 4-footer for par at the 17th.