19-year-old Andrejeva, who won her first Grand Slam title this summer after winning the French Open, won the first set 6-2.
But Coco Gauff hit back in the second set, which was dramatic.
The American took the match to a tiebreak after 7-6 (9-7). The 22-year-old was superior there, winning 6-2 and reaching the semifinals, where newly crowned world number one Jelena Rybakina from Kazakhstan awaits.
For me it was important to play as well as I could, and the crowd helped me, says Coco Gauff.
In the other semifinal, Belarusian Aryna Sabalenka will face American Jessica Pegula.
