Gauff grinds past Kostyuk to reach Australian Open semi-finals
The American fourth seed wore down the Ukrainian in hot conditions on Rod Laver Arena to clinch a scrappy encounter 7-6 (8-6), 6-7 (3-7), 6-2 in three hours and eight minutes.
She will face either defending champion and second seed Aryna Sabalenka or ninth-seeded Barbora Krejcikova on Thursday for a place in the final.
After showing ominous form to race into the last eight, it was a far from convincing display by the 19-year-old, who struggled on serve and fluffed countless opportunities.
"I think today was definitely a 'C' game, so didn't play my best tennis but really proud that I was able to get through today's match," said the 19-year-old, who had never been past the fourth round at Melbourne Park in four previous attempts.
"Hopefully got the bad match out of the way and I can play even better."
The low standard came from both players, with an incredible 16 service breaks throughout the match and the pair racking up 107 unforced errors between them.
Kostyuk will rue missing her chances, letting slip a 5-1 lead and squandering set points in the first set.
The American also faltered at crunch moments, broken when serving for the match at 5-4 in the second set before keeping her cool as Kostyuk became more agitated in the deciding set.
"I was just trying to get one more game in the first set and at least make it competitive and then one game turned to another and I was able to win that set," she said.
"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."
The win extended Gauff's unbeaten streak this year to 10 matches after she won at Auckland in the lead up.
She is into the semi-finals without facing a seed after a string of top names crashed out of the tournament early.