Gauff, who turned 20 on Wednesday, needed 94 minutes to defeat her 25-year-old counterpart in their first career meeting.
With her semifinal slot secured, Gauff improved from her previous best showing at Indian Wells.Furthermore, her quarterfinal win saw Gauff make her third win after trailing in the tournament. In her previous matches against Clara Burel and Lucia Bronzetti, Gauff overcame deficits on her way to victory.
After winning the first set against Yuan, Gauff trailed 3-1 in the second – facing three break points in a crucial fifth game that would have put her down 4-1. Gauff, however, managed to win from a four-deuce service game to keep Yuan at bay.