Safina, the No. 1 seed, eliminated Roberta Vinci of Italy 6-4, 6-4 and Williams, seeded second, defeated Kaia Kanepi of Estonia 7-5, 6-4.
Three seeded Russian players were among others who advanced. Fourth-seeded Elena Dementieva whipped Germany's Anna-Lena Groenefeld 6-4, 6-4, sixth-seeded Svetlana Kuznetsova outlasted China's Jie Zheng 7-6 (7-3), 7-5 and Vera Zvonareva, No. 7, routed Romania's Sorana Cirstea 6-2, 6-2.
Spaniard Maria Jose Martinez Sanchez upset fifth-seeded Caroline Wozniacki of Denmark, 6-7 (5-7), 7-6 (7-2), 6-0.
The ninth-seed, Belarusian Victoria Azarenka, beat countrywoman Olga Govortsova 6-1, 6-3 and No. 14 Marion Bartoli of France ousted Slovakia's Magdalena Rybarikova 6-2, 4-6, 6-3.
Others advancing included Ekaterina Makarova of Russia and China's Shuai Zhang, both unseeded.
Swim Week Miami Beach 2014 [PHOTOS]