Williams, the world No. 1, fired seven aces in her 6-3, 6-3 dismantling of Japan's Ayumi Morita of Japan at Crandon Park.
Her next opponent will be 13th-seeded Dominika Cibulkova of Slovakia, who advanced with a 6-3, 6-4 verdict over Switzerland's Romina Oprandi.
Defending Miami champion Radwanska barely survived her third-round match against Slovakia's Magdalena Rybarikova, hanging on for a 7-6 (7-5), 2-6, 6-3 victory.
She goes on to face 16th-seeded Sloane Stephens, who moved on in a walkover when former world No. 1 Venus Williams withdrew due to a lower back injury.
Also logging a victory Saturday was fifth-seeded Li Na of China, who bounced American Varvara Lepchenko 6-2, 6-4. Ninth-seeded Caroline Wozniacki of Denmark fell 6-2, 6-4 to Garbine Muguruza of Spain.
Other third-round winners Saturday included 30th-seeded Belgian Kirsten Flipkens and Croatian wild card Ajla Tomljanovic.