Aiming to become the first player since Naomi Osaka three years ago to win back-to-back majors, Gauff had breezed into the Australian Open last eight with a series of clinical and composed performances.
However, her display against world number 37 Kostyuk – the highest-ranked player she has faced so far – was far from convincing.
Both players looked tight and tense in a match where they made 107 unforced errors in a total of 246 points.
The three-hour contest featured 16 breaks of serve and Gauff took nine of them – including three in the decider.
The teenager has looked a different proposition over the past six months, playing with more confidence and trust in her ability under the guidance of renowned coach Brad Gilbert.
Showing more faith in her previously shaky forehand has been a key factor in her renaissance after a chastening first-round exit at Wimbledon last year.
Since then, Gauff has lost only four matches and remains unbeaten at the start of the 2024 season.
But that old failing reappeared, particularly in the second set, as Gauff had to dig deep to find a way past Kostyuk.
On her resilience, Gauff said: “I was just trying to get one more game in the first set, make it competitive and then one game turned into another.
“In the second, I gave myself opportunities but became a little bit passive and when I came out in the third I was just trying to play aggressive and hit through the court.”
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