She will face compatriot Diana Shnaider or Polish qualifier Maja Chwalinska, who were playing later, in Saturday's final.
Andreeva, 19, converted her first match point when serving for the match but there was no handshake between them and Kostyuk walked off quickly, turning only to wave and blow kisses to the crowd on Court Philippe-Chatrier, where some fans were draped in Ukrainian flags.
"I am happy that I am in my first ever Grand Slam final. All of these feelings combined, it is amazing," Andreeva said. "I just told myself no matter what happens, I am going to fight and give my best. With this kind of mindset, I ended up winning."
The atmosphere beforehand on Thursday was somewhat tense as the players had separate photos taken as they each stood next to two children on their respective side of the net. Usually the players pose for the same photo, standing right next to each other by the net.
Kostyuk and countrywoman Oleksandra Oliynykova have spoken out during the tournament about the impact Russia's invasion of Ukraine is having on their country.
Andreeva saved three break points at 0-40 in her opening service game, then raced into a 4-0 lead with a flurry of blistering forehand winners.
There was a big cheer when Kostyuk held serve in the fifth game, but the Ukrainian then handed Andreeva the first set when her backhand hit the net.
The semifinal began amid sunny conditions and an open roof, like on Wednesday when beaten quarter-finalists Aryna Sabalenka and Anna Kalinskaya complained of swirling wind on Chatrier and said the roof should have been closed.
It was closed toward the end of the second set of Thursday's semi, offering Kostyuk better conditions for her clay-court game. She broke back to trail 4-3, prompting huge applause and loud chants of "Marta, Marta".
But she dropped her next service game and the comeback ended almost as briefly as it began, along with Kostyuk's 16-match winning streak on clay.
"Obviously, she (Kostyuk) has had an amazing season. Until this match, she has not lost a match on clay," Andreeva said. "She is an amazing player and a very tough opponent."
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