And her 6-3 6-4 win sets Venus up for a round-of-16 clash with Anastasija Sevastova, who defeated 12th seed Julia Georges 6-3 6-3.
It was far from convincing for Wozniacki, who prevailed 6-4 2-6 6-3 against Aliaksandra Sasnovich. It was one of Serena's 41 unforced errors, including 17 on the forehand side.
She took the first game behind a swift 118 miles per hour serve, then held serve before breaking Serena in the sixth game to take a 4-2 lead.
Serena was notably featuring in her first competitive event since her Australian Open win and pregnancy that followed, but along with her sister, has had to deal with health issues and injuries in the past. Serena's shot went wide to set up her sister's first match point.
As one would expect from these two, each was full of compliments for the other.More news: Agitators to lay siege to Vidhan Bhavan in Mumbai
"She (Serena) kept roaring back, I'm just lucky that I've played more matches than her right now".
"I really abhor every time we play, but I do enjoy the battle when I'm out there", Serena commented last weekend. "I think as long as I can do that, I will keep getting better". "It's just afterwards I don't like it as much", she said after the match.
"That's, you know, totally gone out of my mind", she said.
"The base of her game is there, which is very good news", he said. "It nearly doesn't matter, but it would just be wonderful to see her do it now".
"Losing is definitely no less disappointing". I wish it were, but it's not. "I just have a long way to go and I look forward to the journey".More news: Kylie Jenner Revealed All The Pregnancy Details You've Been Dying To Know
Serena won her first two matches, while Venus received a first-round bye and won her opening match.
Asked about her plans, she said: "Get ready for the next tournament".
Wozniacki will have her work cut out again against No20 seed Daria Kasatkina, who beat No13 seed Sloane Stephens, 6-4, 6-3.
On the men's side, Borna Coric of Croatia upset No. 13 Roberto Bautista Agut of Spain 6-1, 6-3; Jeremy Chardy beat No. 20 Adrian Mannarino 7-5, 4-6, 6-1 in an all-French matchup; and No. 11 Pablo Carreno Busta of Spain defeated Daniil Medvedev of Russian Federation 6-1, 7-5. But she will have to fight for that place against No10 Angelique Kerber, who beat defending champion, No24 Elena Vesnina, 7-5, 6-2.More news: Warren: 'I'm not running for president'
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