Muguruza, 19, is ranked 96th in the world, but she made the top-seeded Williams work hard for a 6-4, 2-6, 7-5 win that set up a meeting with No. 5 seed Magdalena Rybarikova. Muguruza survived three match points before falling to the seven-time major championship winner.
Rybarikova fought off qualifier Beatriz Garcia Vidagany in the second round 6-4, 3-6, 6-4.
In other second-round matches involving seeded players, Timea Babos surprised No. 4 Channelle Scheepers 6-1, 6-2 and No. 7 Kristina Mladenovic ousted Tatjana Malek 6-2, 6-1.
Czink will face Mladenovic in the quarterfinals, Puchkova will play Jana Cepelova and Niculescu will meet Babos.
Celebrity Families of 2014 [PHOTOS]