Yastremska used to mimic the 23-time grand slam winner's strokes while watching her play and on the eve of the season's first major, even got a chance to meet the legendary American.
Williams has dropped a mere nine games through three rounds - her lowest tally at a major since the 2013 US Open, which she won - but will likely encounter greater resistance the rest of the way.
'I feel like all of women's - not only tennis but sport really owes everything to Billie Jean King, ' the 37-year-old said on court after a 6-2 6-1 win in 67 minutes.
"I kind of liked that".
Yastremska had treatment on her right foot but it was only delaying the inevitable and Williams took just a few minutes to bring up match point after play resumed.
Halep did precisely that in her solid win over Venus, her third in a row over the American. Later on, the champion while talking about the incident to BBC, said, "I thought she did really wonderful".
"I think I have to play similar [to her performance against Venus], if I can. It's good to see that attitude", she added.
She expected a sterner test on Monday against Serena, who is chasing a record equalling 24th Grand Slam at Melbourne Park and has an 8-1 winning record over the Romanian.
"I honestly would love to face the world number one, it will be great", she said.More news: How Meghan Markle Reacted to Stranger Calling Her 'A Fat Lady'
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"Yeah, not easy. I just have to give my best", Halep said.
Williams defeated Yastremska in a 6-2, 6-1 victory on Saturday.
She also noted that when she was younger, "I played against Lindsay Davenport, Martina Hingis, Monica Seles".
Halep's only wins over Serena came in Singapore in 2014 and a walkover in the 2015 Indian Wells.
"You're so young", Williams told Yastremska.
"She played pretty flawless tennis today - only 12 errors", Williams said.
Halep has struggled for form and fitness since her first-round defeat at the U.S. Open last August and came to Australia on a five-match losing streak and without a coach after long-serving Darren Cahill left for "family reasons". Osaka had earlier shown her frustration by, unusually, throwing her racket to the ground to earn a warning and took a tumble on court trying to counter Hsieh's unpredictable shots. Every time I face the sisters is a big challenge for me. Halep broke again to open the second set but this time Williams managed to respond immediately.
"There's no time for that, I'm sorry to say", the Russian responded when asked if she had any sympathy for her opponent. Both women have legitimate claims to being the top player in the game.