Williams was almost as good, losing just five of 32 points on her first serve in a 6-1, 6-4 win over Viktoriya Tomova.
She said: "It definitely surprises me".
The 36-year-old is now on his joint second longest streak of sets won at Wimbledon - his best was 34 between the third round in 2005 to the 2006 final.
"I just hope every match is better". I can't even be mad at myself, because I played up to the level that I can.
Wozniacki's frustration was only increased by the unwanted infestation that landed at Wimbledon during her match. "For my body, it didn't work, no matter how much I worked out, no matter how much I did". It was her 16th straight victory at Wimbledon, although she missed last year's tournament while pregnant.
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On Court One, Serena's sister Venus Williams had to recover from a set down in successive contests to prevail 4-6, 6-0, 6-1 against Romania's Alexandra Dulgheru for a place in the third round.
Also in the women's draw, Dulgheru's fellow Romanian, Mihaela Buzarnescu, cruised through to round three with a 6-0, 6-3 rout of 19-year-old Briton Katie Swan.
"But I told myself "no, you are not going to lose this match".
The tennis star - who has 10-month-old Alexis Olympia with her husband Alexis Ohanian - admits she found it really "tough" in the beginning and shed a few tears because she didn't know how to help her little girl.
Karolina Pliskova advanced to the third round for the first time with a 6-3, 6-3 victory over Victoria Azarenka. Former Wimbledon finalist Agnieszka Radwanska lost 7-5, 6-4 to Czech world number 66 Lucie Safarova.