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The former champion defeated Elina Svitolina 6-3 6-2 in the quarterfinals.
Russian 17-year-old Mirra Andreeva sent second seed Aryna Sabalenka home, while Italian Jasmine Paolini staved off a fightback from fourth seed Elena Rybakina.
The 30-year-old overcame fourth seed Elena Rybakina in just over two hours to become the sixth American woman to claim the crown in Miami.
World No. 2 and top seed Sabalenka came into the contest on a 15-match winning streak in Australia but was outplayed by former Wimbledon champion Rybakina.
Swiatek will next face Sabalenka in the semifinals, while Gauff will lock horns with Pegula for a place in the final.
American Pegula booked a semifinal spot at the season-ending tournament with a 6-3, 6-2 victory over Sakkari.
Djokovic defeated Poland's Hubert Hurkacz 7-6(6) 7-6(6) 5-7 6-4.
Retired Swiss great Federer received possibly the longest ovation of his illustrious career on Tuesday.
Friday's draw at the All England Club pitched women's top seed Iga Swiatek against China's 33rd-ranked Zhu Lin, a potentially tricky first hurdle for the Pole.
The Wimbledon champion said she had been unwell for the last two days and was out of breath during the warm-up before her match against Sorribes Tormo.
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