After her victory, the 23-time Grand Slam champion noticed how emotional Yastremska was after her loss, and as Yastremska wiped the tears from her face, Williams comforted her with a hug and some encouraging words.
Luckily, the seven-times Australian Open victor was on hand to console the 18-year-old as she became tearful after the match, telling her: "You did unbelievable, you're so young...don't cry!"
Yastremska was born in 2000, the year after Serena won her initial major, and grew up cheering for someone she calls "a legend".
"I honestly would love to face the world No. 1", Williams said Saturday, a few hours before Halep defeated Venus Williams in straight sets.
Halep - who trails 8-1 in the head-to-head meetings - admitted she used to be intimidated by Williams, but she is now ready to take on the former world number one.
When pushed further on what she will need to do to oust Williams next week, Halep said: "It's going to be huge challenge for me".
"I kind of liked that".
Halep did precisely that in her solid win over Venus, her third in a row over the American. "That really broke my heart". "I will play against a great champion and I have nothing to lose", said Halep after beating the elder Williams in a match lasting one and 16 minutes.
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"Only 12 errors. Unfortunately, I had nearly three times as many", Venus said. Halep has split her last six matches on hard court.
Williams put on a typically impressive performance as she powered past her Ukrainian opponent, giving away just three games in the process.
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". I will not super think about this because is nothing to think, just go there and play natural and with confidence.
Williams, 37, was seen consoling Dayana Yastremska, 18, Saturday. "I haven't played the world No. 1 since I've been back".
Unlike any of Serena's foes until now, Halep has won a major title, last year's French Open.
She also noted that when she was younger, "I played against Lindsay Davenport, Martina Hingis, Monica Seles".
Right from the start, Yastremska appeared a bit jittery, missing 9 of 10 first serves and double-faulting three times while getting broken in each of her opening two service games.
'I'm going to apologise, ' she sighed. "There's a good chance for me to play my best tennis and to feel good on court". Both women have legitimate claims to being the top player in the game.