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.
Norwegian Getaway cruise ship crew member rescued from ocean off Cuba
The man's identity has not been revealed, and the circumstances surrounding his fall into the water have not been established. The Coast Guard was alerted and started searching for him. "Our condolences to the crew member's family", said Lowinger.
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.