Rybakina, the 2024 Stuttgart winner, needed three hours to get past Fernandez 6-7 (5/7), 6-4, 7-6 (8/6) on Friday, saving two match points in the final-set tiebreak.
Earlier Andreeva rallied past two-time Stuttgart champion Iga Swiatek 3-6, 6-4, 6-3.
“Especially in the beginning there was a lot of frustration. I was just going downhill. The serve was not going,” Rybakina said.
“Somehow I found the fight in me and a couple of points were important in the second set. And somehow I started finding this momentum.”
Swiatek, who had won four of her six Grand Slams on French Open clay, was considered among the favourites but struggled against the energetic Russian.
The Pole capitalised on some clumsy baseline errors from her opponent to win the opening set but Andreeva converted a crucial break point to take the second set.
Swiatek ran out to a two-game lead in the deciding set but Andreeva broke back twice to take the initiative, and the match.
“She’s won so many tournaments I can’t even count how many Slams she’s won… she’s a past winner of this tournament as well,” Andreeva, 18, said.
Earlier Karolina Muchova broke through for a first win over Coco Gauff, eliminating the reigning French Open champion 6-3, 5-7, 6-3 to reach the Stuttgart semi-finals for the first time.
The 12th-ranked Muchova will face Elina Svitolina for a place in the final after the fourth-seeded Ukrainian moved past Czech Linda Noskova 7-6 (7/2), 7-5 to book her semi-final spot.
The in-form Ukrainian has now reached five semi-finals this season. (AFP)
