
Safarova, ranked 36th in the world, moved into the quarter-finals with a 7-6 (7/5), 6-1 victory — her first triumph against a top-10 opponent since 2015.
The 30-year-old Czech will face Dane Caroline Wozniacki, who advanced when Muguruza retired from their match due to illness shortly after losing the first set 7-6 (7/1).
In an all-Czech clash, second seed Karolina Pliskova defeated Barbora Strycova 6-1, 6-4.
Later matches Monday feature American Venus Williams against seventh-seeded Russian and Indian Wells runner-up Svetlana Kuznetsova and world number one Angelique Kerber against Japanese qualifier Risa Ozaki.