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Alcaraz became the first man to defend a championship in the California desert since Novak Djokovic won three straight between 2014 and 2016.
Alcaraz came from behind to beat Jannik Sinner before Medvedev edged out American Tommy Paul 1-6, 7-6(3), 6-2 in the second semifinal.
Sakkari got the better of US Open champion Coco Gauff in a hard-fought second semifinal.
Third seed Coco Gauff served up 17 double faults but still managed to beat China's Yuan Yue 6-4, 6-3 to reach the women's semifinals in the Californian desert for the first time.
Navarro, seeded 23rd, broke the hard-hitting Belarusian for a fourth time on match point to book a quarterfinal clash with ninth seed Maria Sakkari of Greece.
'This is a miracle,' said Nardi, who lost to David Goffin in the qualifiers and only got into the main draw after Tomas Etcheverry withdrew due to injury.
Russians and Belarusians were banned from competing internationally following Russia's invasion of Ukraine in 2022, for which Belarus has been used as a staging ground.
Geneva: Former Wimbledon and French Open champion Simona Halep had her four-year doping ban cut to nine months by the top court for global sport on Tuesday, making the former world number one eligible to return to competition immediately. Halep was initially banned for four years for two separate
Nadal, who has won 22 Grand Slam titles, added that the future of Spanish tennis was in good hands with the 20-year-old.
Humbert became only the third player in the professional era to win his first six tour-level finals, matching the achievement of Latvia's Ernests Gulbis and Slovakia's Martin Klizan.