Tremors were felt in the Greek capital of Athens and as far away as the southern island of Crete
The two-time Grand Slam champion said it was a "difficult match."
"She had a lot of advantages but I'm happy that I kept fighting and ended up winning," said Muguruza, who won the French Open in 2016 and Wimbledon a year later.
Muguruza will next face eighth-seeded Dayana Yastremska, who beat wild-card entry Peng Shuai 6-1, 6-4.
"In the first set, I felt really well on court but in the second set I felt a bit weak," said Yastremska, an 18-year-old Ukrainian. "But I tried to keep myself under control and stayed focused like I did in the first set, which is the key for me to take the second set."
Yastremska beat Muguruza last year in Luxembourg, winning 6-2, 6-3.
"She is young and has nothing to lose," Muguruza said. "She is playing well right now. It will be a tough match."
Also, fourth-seeded Saisai Zheng beat Irina-Camelia Begu 6-2, 6-4 and sixth-seeded Ajla Tomljanovic defeated Kateryn Kozlova 7-6 (0), 6-1.
Tremors were felt in the Greek capital of Athens and as far away as the southern island of Crete
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