The 37-year-old, who is in the hunt for her first Grand Slam since having a baby, comforted the 18-year-old at the net, telling her: "You did wonderful, you're gonna make it, don't cry".
Then they embraced, and Williams patted Yastremska on the back.
"As she was walking towards the net, I could tell she was quite upset", Williams said. "I liked that. It showed that she wasn't just there to play the match, she was there to win".
Beating Williams, however, would make her just the ninth woman to defeat both Venus and Serena at the same tournament. Her opponents, on the other hand, are learning it's tough to win a match while in awe of the woman on the other side of the net. It really broke my heart. That was a good idea for her, I don't think it's a good idea for everyone, but for her it's the right choice. "It's good to see that attitude". Yastremska was seen wiping away tears after losing to Williams 6-2 6-1.
Halep set up the fourth-round blockbuster by sending the 23-time major winner's older sister Venus packing in straight sets.
"She said, like, 'You're young, you're very good and you will be a good player in the future.' It's nice to hear those words from a legend", said the 57th-ranked Yastremska. But for sure she's the best player in the world because she won so many grand slams.
"There's no time for that, I'm sorry to say", the Russian responded when asked if she had any sympathy for her opponent. 'I think that's something that we're going to continue to do, continue to fight for.
"I think I helped her take the best out of herself at a period of time in her career".
"I have to move her and give my best".
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Svitolina, who won last season's WTA Finals, recovered from 3-0 and two service breaks down in the third set against China's Zhang Shuai to prevail.
Serena Williams marched into the Australian Open last 16 on Saturday and warned she was still improving after taking time out to console the latest victim of her quest for a record-equalling 24th Major.
It was all a bit overwhelming for the latest opponent who could do nothing to slow Serena Williams at the Australian Open.
That resume pales in comparison to Serena's, of course. "I'm in a good position".
"I just want to try to play my best tennis", Halep said, "because I have nothing to lose".
As an eight-year-old she had cheered Williams on to an Australian Open title a decade ago from her lounge room in Odessa, even simulating the American's strokes with her own racquet as she watched on television. The most recent meeting was in the 2016 US Open, a match Serena won in three sets.
Halep has won only one of nine previous clashes against the 23-time major victor, all of which took place before Williams took time off tour for the birth of daughter Olympia.
This is Williams's first official tournament since the controversial US Open final, and only her eighth since she came back last March, so sparingly does she play.