World number two Rybakina from Kazakhstan defeated American 28th seed Ann Li 6-2, 7-5 in 90 minutes, winning five of six break chances while saving two of four against her.
Rybakina, who also won the 2022 Wimbledon title, advanced to a last-16 meeting with the winner of a later match between Russia's Liudmila Samsonova and Australian Maya Joint.
Fernandez, the 30th seed, dispatched 19-year-old Russian fifth seed Andreeva 6-1, 6-4 in 80 minutes.
Fernandez won 24 of 27 points on her first serve and captured 17 of 23 points on Andreeva's second serves to advance.
The Canadian will next face the winner of a later match between four-time Grand Slam winner Naomi Osaka, the 11th seed from Japan, and Belgium's 20th-seeded Elise Mertens.
Also advancing was 19-year-old Russian Alina Korneeva, who ousted US 13th seed Iva Jovic 6-3, 6-4. Korneeva won seven of eight break points to reach the last 16 after 82 minutes.
Next in Korneeva's path will be the winner of a night match between US fourth seed Coco Gauff and Greece's Maria Sakkari.