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Gauff, a three-time winner at WTA 1000 events, was contesting her first quarter-final in Miami after last-16 exits in 2022, 2024 and 2025.
She will meet Karolina Muchova for a place in the final, after the Czech defeated Canadian teenager Victoria Mboko 7-5 7-6 (7-5).
If Gauff reaches the final, she will overtake former world number one Iga Swiatek and move to third in the WTA rankings next week.
Australian Open champion Elena Rybakina, runner-up to world number one Aryna Sabalenka at Indian Wells earlier this month, set up a quarter-final against fifth seed Jessica Pegula.
The world number two ended Australian 21-year-old Talia Gibson's impressive run in a 6-2 6-2 victory.
In Wednesday's other quarter-final match, defending champion Sabalenka will take on American Hailey Baptiste.
