Second seed Aryna Sabalenka of Belarus survived a scare as she overcame British wildcard Katie Boutler 4-6, 6-3, 6-3 to reach third round, even as world No. 7 Bianca Andreescu of Canada was shocked 6-2, 6-1 by France's world No. 58 Alize Cornet.
Aryna, who is the world No. 4, committed 30 unforced errors but she converted five of the six break points as against three out of 12 by Katie. She fired 11 aces to Katei's three and won 67 per cent of first service points.
No.3 seed Elina Svitolina of Ukraine survived a scare in first round as Alison van Uytvanck of Belgium stretched her. Elina won 6-3, 2-6, 6-3.
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Anastasia Pavlyuchenkova, the 16th seed and Czech Republic's Karolina Muchova, the 19th seed, won their delayed first-round matches on Wednesday.
The Russian Anastasia beat Ana Bogdan of Romania 6-2, 6-2 while Karolina thumped Zhang Shuai of China 6-3, 6-3.
Elina, who had become the first Ukrainian woman to reach a Grand Slam semi-final at the last Wimbledon, needed one hour and 41 minutes to beat Alison.
"I think the return was quite good for me today," said Elina in her post-match press conference.
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"I was striking the ball really good. On important moments, I think I was calm and my shots were quite good in the end. Just happy the way I was tracking the ball and that I could hold my nerves. This was very important for me today."