WTA Finals: Jessica Pegula saves match point to beat Linda Noskova, Coco Gauff out
Earlier, Gauff had shown all of her battling qualities as she fought through injury to beat Kostyuk.
The American received treatment on her lower back midway through the match and soon found herself 5-1 down in the second set.
However, the world number four rallied and reeled off six games in a row to complete a 6-4 7-5 win.
“Physically, I wasn’t at my best, which I’m not really used to,” Gauff told Sky Sports.
“It was like a mental challenge, learning how to play through that.”
The long tennis season has taken a toll on a number of players, with Ukraine’s Kostyuk also receiving treatment on a wrist injury that has been hampering her since August.
It is the second time that Gauff has overturned a 5-1 deficit at this tournament, having done the same to beat Pegula on Sunday.
However, the 22-year-old admitted she was not expecting it to happen again, and was already preparing herself for a third set.
“I asked my physio at 5-2 down, what can I do on the bathroom break [between sets] to try and loosen up,” Gauff said.
“And then there was no bathroom break!”
Gauff struggled with her serve throughout, producing nine double faults to one ace, but said afterwards she struggled to get through her motion without feeling pain.
Kostyuk – a late call-up to the season-ending finals after Elena Rybakina’s withdrawal – also struggled to generate pace and spin because of her wrist problem.
World number four Gauff came back from an early break down to take the first set, but immediately ran into problems in the second.
She called for the trainer after going 3-0 down but soon trailed by a double break, with Kostyuk saving three break points inbetween.
However, with her movement hampered and the crowd behind her, Gauff was able to swing hard and ultimately outlast Kostyuk.