The 23-year-old Kostyuk dedicated her victory to the Ukrainian people as tears rolled down her cheeks during the on-court interview.
"I want to start with this historical match I played with Elina. We had a difficult night in Kyiv, so many people dead. So I give this match to the Ukrainian people and their resilience. Slava Ukraini," the 15th seed said.
"I want to point out Elina and her impact on Ukrainian tennis, on me and on everyone watching. She's an unbelievable fighter. I'm so happy to be through, but I want to thank her for this incredible match."
Kostyuk surged into a 4-1 lead under the closed roof of Court Philippe Chatrier before Svitolina clawed a break back in front of a sparse crowd.
But Kostyuk broke again to move 5-3 ahead and sealed the opening set when seventh seed Svitolina sent a forehand long.
The momentum shifted in the second set as Kostyuk's serve deserted her, allowing Svitolina, who has now lost in the quarter-finals at Roland Garros for the sixth time, to level the contest.
The decider turned into a tense scrap, with the first five games going against serve.
Pointing her index finger to her head after finally holding for a 4-2 lead, Kostyuk steadied herself before another break and a comfortable hold secured victory and a last-four clash with Russia's Mirra Andreeva.