Sakkari, the Greek ninth seed, scored a 6-7 (3-7) 6-4 6-2 victory in two hours 52 minutes on Tuesday to set up a final-four showdown with Aryna Sabalenka.
Already a first-time quarter-finalist in the Spanish capital, Sakkari is now through to her eighth career WTA 1000 semi.
The two Top 10 players will meet for the ninth time, with Sabalenka holding a 5-3 edge. All eight of those meetings, though, were played on hard courts.
They've already played once this year, with Sabalenka winning 6-2 6-3 last month in the semi-finals of the BNP Paribas Open.
"She's the one that is playing the best tennis right now, better than anyone else. Obviously it's not hard court, her favourite surface, but she won this tournament and she's playing very good," Sakkari said.
"I believe I can play good on clay court, I believe I can play good here. Let's see how it goes. I'm very curious to see how different it will play compared to other times we've played each other."
Earlier, world No.2 Sabalenka denied unseeded Mayar Sherif the biggest victory of her career, also rallying from a set down to win 2-6 6-2 6-1.
Sabalenka made 37 unforced errors, but the Australian Open champion bounced back midway through the second set to win 10 games in a row and take control.
The Belarusian saved a set point at 5-1 but Sherif, who has won just one WTA 250 title in her career and was playing in her first WTA 1000 quarter-final after beating three seeded players, served out to take the opening set.
The Egyptian took the lead in the second set too before Sabalenka, who was a break down, finally found her groove to break four times and force a decider.
The 2021 champion then raced into a 5-0 lead in the third before Sherif got on the board.
"Honestly I was just trying to keep fighting and keep playing my game," Sabalenka said.
"She played unbelievable tennis, she's a claycourt specialist and I'm very happy with this win."
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