The 2023 champion had none of her usual firepower at first and was on the ropes in the tiebreak before she flipped the script and closed out the match with a forehand strike, dropping her racket to the court in joy and relief.
She faces second seed Elena Rybakina in the last four.
Andreeva looked completely at home in Arthur Ashe Stadium as she sprinted through the first four games, never allowing Gauff to set up a break-point chance in the opening set, where the Russian had just five unforced errors to 14 from her opponent.
The two players settled into a fine fight in the second set, trading breaks twice before the tiebreak, where Gauff deployed a perfectly placed backhand to win a 39-shot rally and twice saved match point.
Andreeva flung her racket at her bench in disgust after dropping her serve in the third game of the decider, and Gauff broke her to love in the seventh game to put the contest completely out of reach.
Check out the game summary with Flashscore.
More to follow.