Rybakina was more efficient than Keys, winning just over 80% of her first serve points and converting three of her eight break points during the 84-minute encounter.
"Really happy with my performance today," Kazakhstan's Rybakina said in her on-court interview. "It was a tough one.
"With Madison it's always difficult matches and she's an aggressive player so I knew that I needed to be ready for every point and especially on the return."
Rybakina, who due to illness withdrew before her first match at Indian Wells where she was the defending champion, now moves on to the eighth quarter-final in her last 10 WTA 100o events.
In other early women's action, Kazakhstan's Yulia Putintseva beat Ukraine's Anhelina Kalinina, the 32nd seed, 6-4, 7-6(5).
Sakkari was scheduled to play in the day's opening match on the Grandstand court but advanced without hitting a ball as Russia's Anna Kalinskaya withdrew ahead of their fourth-round match due to health issues.
Kalinskaya, the 22nd seed, arrived in Miami following a third round defeat at Indian Wells where a stomach ailment forced her to miss a few days of practice.
The 25-year-old Kalinskaya reached the round of 16 in Miami without dropping a set in wins over China's Wang Xiyu and Latvian ninth seed Jelena Ostapenko.
"I'm so sorry I was really looking forward to playing today, but unfortunately my health doesn't allow me. Thank you for your support," said Kalinskaya.
Rybakina owns a 2-1 record in head-to-head meetings with Sakkari, who arrived in Miami fresh off her loss to world number one Iga Swiatek in the Indian Wells final.
"Tough opponent and I'm going to try to do my best to prepare as much as I can and try to be fresh physically," said Rybakina. "I think it's going to be a tough one but hopefully it goes my way."
