Choi birdied the next hole, danced around a few more potential pitfalls on the back nine, and went on to win by 4 strokes Sunday at Blackwolf Run.
It's the first major and sixth career LPGA Tour victory for the 24-year-old South Korean star, who came into the tournament ranked fifth in the world.
Choi shot a 1-over 73 on Sunday and finished at 7 under. Yang, also from South Korea, had a 71 to finish second.
Choi's victory comes at the same course where Se Ri Pak won the Open in 1998, a victory that inspired Choi and many other young South Koreans to try to make it on the women's tour.
"And 14 years later I'm here right now, and I made it," Choi said. "My dreams come true. It's an amazing day today, and like I really appreciate what Se Ri did and all the Korean players, they did. It's really no way I can be here without them."
Pak was among a group of friends who met Choi after she putted out on the 18th green, showering her with hugs - and victory champagne.
"[Pak said], 'Hey, Na Yeon, I'm really proud of you. You did a really good job, and you [were] really calm out there,' " Choi said. "She talked to me a lot, and she was hugging me."
Choi is the fourth South Korea player to win the event in the five years, following Inbee Park (2008), Eun-Hee Ji (2009), and So Yeon Ryu (2011).
And while Choi's performance on the 10th wasn't pretty, she could afford to have one bad hole Sunday thanks in large part to her remarkable performance Saturday, when she matched the fifth-lowest round in Open history with a 65.
Choi and Yang were the only players to finish the tournament under par.
Yang was expecting Choi's best effort.
"I knew she was going to play well," Yang said. "She's very consistent player."
Sandra Gal of Germany shot a 74 and finished at 1 over. Il Hee Lee of South Korea, Shanshan Feng of China, and Italian Giulia Sergas finished 2 over.
Michelle Wie finished at 10 over. After shooting a 66 on Friday to close within a stroke of the lead, she had weekend rounds of 78 and 80.
"Contention for me kind of got my juices flowing and kind of made me want it more and felt like what it was like again," Wie said. "So I'm really looking forward to the next tournament, and there's a lot of positives to take from this week."
Top-ranked Yani Tseng finished 14 over, and still needs an Open victory to complete a career Grand Slam.
The afternoon belonged to Choi, who was even through the front nine, making bogey on No. 1 and making a birdie putt on No. 4.