Andreeva, ranked world No. 194 and a wildcard for the tournament, beat world No. 19 Magda Linette 6-3 6-3 on the clay in Spain.
Earlier in the week, Andreeva had already become the seventh youngest player this century to beat a top 20 player, according to the WTA, beating world No. 14 Beatriz Haddad Maia in straight sets in the second round.
The Russian was runner-up at this year’s junior Australian Open and now has 16 professional wins to her name.
Her next opponent is reigning Australian Open champion Aryna Sabalenka. Victory over Sabalenka, the world No. 2, in the fourth round Monday and the teenager’s name will undoubtedly become more widely known.
The Russian’s rise has been so rapid that she has no picture or biography yet on the WTA website.
“I didn’t expect to be here and playing Sabalenka in the round of 16,” Andreeva told the Tennis Channel, according to the WTA.
“I’m not really surprised with my level, because I know the way I can play on the court … but of course, I didn’t expect to be here and go this far.”
The Russian said she had “nothing to lose” against Sabalenka.
“I just have to go there and show the best tennis I can,” she said. “There is no pressure at all for me.
“There is some pressure on her, I think, because she’s going to play a 16-year-old girl. Most probably, we will play on some stadium, so I’m excited to do that.”