Lee gained the finals with a 1-up win over Elizabeth Dotson in the quarterfinals and a 5-and-4 conquest over Jane Rah in the semifinals.
Chudy outlasted Amie Cochran 1-up in 19 holes in the quarters and bested 2004 champion Ya-Ni Tseng, 4 and 2, in the semifinals to move into the final match.
Lee gained 1-up leads after wins on the third and fifth. However, Chudy fought back both times with wins on the fourth and sixth when Lee stumbled to bogeys on both holes.
The 19-year-old Chudy gained her first lead with birdies on nine and 10. Lee then birdied the 11th to get back within 1-down, she bogeyed the 13th and Chudy birdied the 15th to move 3-up.
Lee's bogey on No. 18 dropped her 4-down after the opening 18 holes. The duo halved the first four holes of the second 18 holes.
'I knew being 4-up in the morning 18 didn't mean I won the match,' said Chudy. 'I knew it could be taken away from me easily, especially if she got on a good streak or I started struggling. Unfortunately, both things started happening.'
Chudy birdied the 23rd hole to gain her biggest lead at 5-up. The 17-year-old Lee fought back with three birdies over the next four holes to get back to 2- down after 27 holes.
Lee got it to 1-down with a birdie on the 30th hole, but her run was halted as she bogeyed the 31st hole. Lee, though, bounced back with a birdie on the 34th hole to get to 1-down.
Chudy was unable to save par on the 36th hole and Lee's par meant the match would go extra holes. Chudy bogeyed the first, playing as the 37th hole, to give Lee the championship.
'I thought chances would come,' said Lee through an interpreter. 'I had confidence that I could do it. I am so happy right now.'
Lee receives a 10-year exemption into the Women's Amateur Public Links and exemptions into the next two U.S. Women's Amateurs.