The Russian-born Austrian defeated former world No.1 Karolina Pliskova 6-1 6-7 (4-7) 6-3 in the Madrid Open quarters on Wednesday, eight days since she'd been knocked out of qualifying at the Caja Magica.
Potapova capitalised on her unexpected main draw entry to stun the Czech in a roller-coaster clash, despite squandering three match points.
The 25-year-old's dream run has included startling victories over former French Open champion Jelena Ostapenko and world No.2 Elena Rybakina.
Asked if she had thought she would be in the final-four after her qualifying loss, the unseeded Potapova said: "No, I wouldn't, for any money and anything.
"That's what makes our sport beautiful. I was given a second chance and now I'm here.
"I'm super happy. There's nothing better that could happen to me in my life at the moment."
After cruising through Wednesday's opening set, Potapova appeared destined for a straightforward victory when she earned three match points in the second.
But Pliskova clawed her way back to force a tiebreak and level the match.
Potapova then trailed 3-1 in the decider, only to reel off five consecutive games and seal victory with her 10th ace before collapsing to her knees.
"I was given a few match points in the second set on serve. I couldn't manage my nerves at the time, I know that," Potapova said.
"But it seems like this tournament keeps giving me second chances and I keep using them."
Potapova will face Marta Kostyuk in the semi-finals after the Ukrainian beat Linda Noskova 7-6 (7-1) 6-0.
Kostyuk defeated Potapova in the fourth round last year in Madrid, and is undefeated on clay this year.
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