The Ukrainian 26th seed created 23 break point opportunities on Noskova's serve, and broke the Czech seven times en route to her second 1000-level semi-final and first in Madrid.
There was nothing to choose between the two players in the first set, with Kostyuk edging a gruelling 65-minute battle in a tiebreak.
However, the contrast in the second set couldn't have been greater, with the Ukrainian not losing a single game and wrapping it up in just 24 minutes.
As a result, she extended her winning streak to 10 matches, and maintained her 100% clay-court record in 2026.
Next up for her is Potapova, who Potapova reached the first WTA 1000 semi-final of her career with a hard-fought 6-1, 6-7 (4), 6-3 win against former world number one Karolina Pliskova.
Having recently switched allegiance from Russia to Austria, Potapova is the first player representing Austria to reach a WTA 1000 semi-final, and the first lucky loser to make it this far at a tournament of this level.
Kostyuk, along with her compatriots, does not shake hands with Russian and Belarusian players ever since the war in Ukraine started four years ago. Asked if Potapova changing her nationality to Austrian will change her stance when they square off on Thursday, she said:
"The only person that I shake hands with is Daria Kasatkina, because she didn't just change her passport, she also openly said that she doesn't support the war and all of that stuff.
"So this is why me and like other girls made the decision to shake hands with her, purely out of respect.
"In this case, I mean, there have been multiple players who have changed their nationality, but none of them ever voiced anything against war or anything to support Ukrainians. So for me that doesn't change."