Madrid
The 20th-ranked Czech was a semifinalist at the Australian Open, which was won by Osaka in February.
"It was a tough match today, but we had some preparation,” Muchova said. “I was ready to play with all I had today, and to use all the weapons I could and (do) what I can."
Osaka was coming off a quarterfinal loss to Maria Sakkari in Miami.
"On the third set I felt I just started off really bad and I couldn't afford to do that,” Osaka said.
Muchova next faces 16th-seeded Sakkari, who defeated Anett Kontaveit 6-3, 6-1.
Anastasia Pavlyuchenkova beat sixth-seeded Karolina Pliskova 6-0, 7-5, while fifth-seeded Aryna Sabalenka defeated Daria Kasatkina 6-3, 6-3.
In the men's draw, 11th-seeded Denis Shapovalov won 90% of his first-serve points to beat Dusan Lajovic 6-1, 6-3 and reach the second round. American Tommy Paul defeated Pedro Martínez 6-4, 7-5.
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