The 29-year-old, whose mother was born in Seoul, won 6-2, 6-3 for her fourth career victory and second this season following Montreal in August.
Pegula, the world number four, also made the finals in Doha and Tokyo this year.
“My mom is Korean and she was adopted from here so it’s really special to be able to win here,” said Pegula.
“In the last few years, as my ranking has gone up, I’ve definitely felt so much more support from the fans, a lot more than I expected coming back here from five years ago. So it’s really special.”
Pegula, who reached a career-high world number three last year, has never managed to get past the quarter-
finals in each of the four Grand Slams.
Yuan, the 128th-ranked player in the world, reached her first WTA final after never making it past the quarter-final stage before this week.
“Our last game was a battle, and this one was too,” Pegula remarked of their second encounter.
“You’re really skilled, and I told you your rating will rise. You said it was your first final, but I’m sure you’ll have many more.