Czech Republic's Karolina Pliskova reacts after a point against Paraguay's Veronica Cepede Royg
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In a match of just three break points between two Czech seeds, it was the former world number one who held her nerve on Court 3.
"It's tough to play another Czech player especially as we are Fed Cup team mates," Pliskova said on Margaret Court Arena. "It's always close but I served well and that's the key for me."
Pliskova will next meet either 20th seed Barbora Strycova or Bernarda Pera.
Stage 7, Vasto - L'Aquila (185km)