Williams knows what it's like to be the one weeping after a loss, so she put her right hand on Yastremska's shoulder and consoled her by saying, "You're so young".
The 37-year-old Williams, chasing a record-extending eighth Melbourne title in the professional era, barely broke sweat on a sunny afternoon at Rod Laver Arena as she racked up 20 winners and beat the 57th-ranked 18-year-old in a breezy 67 minutes.
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.
The American has an 8-1 grip on that rivalry, but the Romanian comes into the match after beating her sister, Venus, fairly convincingly on day six, 6-2, 6-3 in a little more than an hour-and-a-quarter. "I'm telling you, she's going to give Serena Williams trouble".
"I kind of liked that".
She was listless in her first two matches, complaining she was not at her best and grinding out three-set wins. With wins in 12 of her last 13 sets when you include the Hopman Cup, it's clear to say that Serena is in great form and should be considered the overwhelming favorite to win this title. Later on, the champion while talking about the incident to BBC, said, "I thought she did really incredible. It's good to see that attitude".
In the second week of the tournament, Williams and Halep will play Monday in Melbourne, but their match is Sunday at 7 p.m. ET.More news: Phoenix police: Dead newborn found in Amazon site's restroom
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"I was ... struggling", said Svitolina, who was treated by a trainer after the second set.
"If she thinks so", Yastremska added about Williams, "then maybe that's true". You also have to question how much Halep has left in the tank considering she has only a few matches under her belt since September.
"I honestly would love to face the world No. 1", said Williams.
Serena Williams recalls being in the position of young Dayana Yastremska, an ambitious and highly talented teenager overcome with emotion in the disappointment of defeat.
"I thought she played wonderful, came out swinging". Every time I face the sisters it's a big challenge for me.
"She played pretty flawless", said Venus, who exits before the fourth round at a fifth consecutive Grand Slam tournament. "I will not super think about this because there is nothing to think, just go there and play natural and with confidence".
Further afield if Williams prevails, potentially, are players who have downed Williams at grand slams, Garbine Muguruza, Karolina Pliskova and Naomi Osaka.