Osaka looked a total shadow of the player who has won the last two Grand Slams and risen to the top of the world rankings as she was bageled by Schmiedlova.
"John is a tough player who beat Federer so I knew it would be hard", said Zverev, bidding to become the first German man to win the Roland Garros title since Henner Henkel in 1937.
Later Tuesday, defending champion Simona Halep faces Australia's Ajla Tomljanovic, the world number 47, who reached the fourth round in 2014.
Osaka recovered her composure for a break and a 3-0 lead in the second set but a brief suspension for rain disrupted her composure and allowed the Slovakian to hit back to 3-3.
Osaka said she had only practiced on the cavernous Court Philippe Chatrier for 30 minutes since her arrival in the French capital. My training has gone well and I played a good tournament in Rome, which was very important for my confidence. "And then I think she got very lucky at the start of the second set and took advantage of the opportunities she got", Wozniacki said, her chin resting on her left hand.
Perhaps she was helped by, before the tournament, stating her intention to win it, out loud and on the record.
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The former Australian Open victor and 13th seed, who has yet to win a match on clay this term, fell away badly after a strong first set, but claimed that an injury had also hampered her preparations.
But the calf problem hampered her preparations for the French Open even if she did not feel any pain on Monday.
Summed up Zverev, who had 57 winners and 73 unforced errors: "I'm through - and that's all that matters". "And then instead of correcting it, I just kept getting worse".
"It's definitely frustrating. You want to win, you're competitive, you work hard, and you want to see results".
"You get hurt, you get injured, and you just have to try to work through that".
"Roland Garros-that's, for me, what I'm dreaming about right now", Osaka said. "And sometimes you're just unlucky as an athlete", she said.