For the first time in the professional era, four women from the Czech Republic reached the last 16 of a grand slam and Safarova could be joined in the last eight by compatriots Barbora Zahlavova Strycova and 2011 champion Petra Kvitova, who are in fourth round action later on Monday.
Safarova, seeded 23rd, needed just 48 minutes to end Smitkova's bid to become the lowest-ranked woman to reach the quarter-finals.
She will next meet either Polish fourth seed Agnieszka Radwanska or Ekaterina Makarova of Russia for a place in the semi-finals.
(Reporting by Pritha Sarkar; Editing by John O'Brien)
- Sports & Recreation
- Lucie Safarova
- Petra Kvitova
- Barbora Zahlavova Strycova