The Russian-born Austrian, who lost in qualifying last week, has capitalised on her unexpected main draw entry, stunning former world number one Pliskova in a roller-coaster clash despite squandering three match points.
Potapova's run has included impressive victories over former French Open champion Jelena Ostapenko and world number two Elena Rybakina.
When asked if she thought she would be in the final four after that 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 the opening set, Potapova appeared destined for a straightforward victory when she earned three match points in the second.
But Pliskova clawed back to force a tiebreak and level the match.
Potapova 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 or Linda Noskova in the semi-finals.