Returning after more than a year away from the game to have a baby, Serena put up a good fight, saving match point while trailing 5-2 in the second set, but her rustiness told in the end.
While she had numerous unforced errors and eight double faults, the No. 8 seed did enough to advance. Serena leads 17-11 - and has claimed five of their past six meetings.
Wozniacki, who will face 20th seed Daria Kasatkina for a spot in the quarter-finals, said: "I was struggling finding my rhythm". Despite some nerviness and almost squandering a double break lead in the second set, Venus closed it out what was a relatively routine victory.
Serena Williams is set to launch her own cosmetics line under the name "Aneres", which is Serena spelled backwards. "You know, we can always stay in the tournament longer if the both of us are in the tournament", Serena said. So, I'm going to wait and see what happens.
Ellie Sullivan, 10, of Dallas, left, and her mother, Andrea Sullivan, hold up signs for Serena and Venus Williams during a break as the sisters face one another in the third round of the BNP Paribas Open tennis tournament at the Indian Wells Tennis Garden in Indian Wells, Calif., Monday, March 12, 2018.
Presently unseeded Serena was the world No.1 when she began her long vacation from the game, following her victory at the 2017 Australian Open, where she was already expecting daughter Alexis Olympia, who was born in September.
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And she expressed her frustration at her display. "Maybe I'll write everything down and rank them so that I know what to work on first going into Miami". First of all, 17 years ago seems like forever ago.
"She looked like she never lost a step", Venus said of her younger sister.
But Serena says she did not watch a single point on the grounds she gets too nervous.
"I still have a lot to give".
I really hate when Serena loses.
Danielle Collins also won her third round match, defeating Sofya Zhuk of Russian Federation 6-4, 6-4.
In other women's third round matches on Monday, French seventh seed Caroline Garcia defeated Australia's Daria Gavrilova 7-5, 6-4.