The Czech beat Kostyuk in straight sets en route to the title at the grasscourt major this year but endured a far tougher encounter at Louis Armstrong Stadium, finally sealing victory on her sixth match point with an unreturnable serve.
"I am more than relieved. This match was so tough. I mean, emotionally, more than physically," said Noskova, who crumpled to the court as she finally got over the finish line. "I feel like a huge rock fell off my heart at the end."
The sixth seed used her rock-solid backhand to blunt her opponent's serve in the opening set and produced a couple of fine forehand winners en route to the decisive break in the 11th game.
Kostyuk's troubles deepened in the second set as two double faults and an unforced error handed Noskova a break in the seventh game.
The Ukrainian slumped over and buried her face in her hands after sending a shot wide in the eighth, but the fans rallied around her, sparking a revival that saw her save two match points and swat a shot past Noskova to pull level at 5-5.
Kostyuk then broke her opponent to love in the 12th game to force a deciding set, but could not sustain the momentum. Noskova moved 4-3 ahead with a superb backhand winner, and Kostyuk repeatedly boiled over with frustration.
"Today was very close. It could have ended both ways," said Noskova.
