The Olympic gold medalist from Switzerland beat Iga Swiatek 7-6 (12), 6-3 to make the last eight in Flushing Meadows for the third time.
Daniil Medvedev, representing the Russian Olympic Committee (ROC) team since Russia is banned, also won his first-round match against Alexander Bublik of Kazakhstan 6-4, 7-6(8).
The Tunisian converted all seven break points she created and served out the match at love with an ace.
If Gauff wins, she will be the youngest American woman to reach the final four in Paris since Jennifer Capriati was 14 in 1990.
Sakkari had beaten No.4 seed Sofia Kenin in straight sets on Monday before Swiatek had to battle against Marta Kostyuk for her 6-3, 6-4 win.
Swiatek has now won 22 straight sets at Roland Garros, including her run to the title last year.
After seven days of breathtaking action on la terre batteu, 32 players, on either side of the singles tournament await their fate as round of 16 begins from Sunday evening
Swiatek dispatched Rebecca Peterson of Sweden, 6-1, 6-1 in one hour and one minute to progress while Kenin beat American compatriot Hailey Baptiste 7-5, 6-3.
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