Serena Williams bosses the head to head between the two players. The game looked bleak for Venus as Halep claimed a third successive break to open the second set.
The 27-year-old defeated Venus 6-2, 6-3 in an imperious fashion in the match that lasted more than an hour.
Svitolina had a medical time-out and several courtside massages for a shoulder complaint during the marathon match on Rod Laver Arena.
"She said "don't cry, you're still young. come on you don't have to cry", the Ukrainian said. 37-year-old Williams was heard telling Yastremska, reminding her opponent that she's only a teenager still. It really broke my heart. "I couldn't help it". I just do the work, I go out there and I play the best I can.
She told Yastremska, who was born in 2000, a few months after Williams won her first Grand Slam at the 1999 US Open: "You're so young".
After two tough three-set tussles, Halep had a much easier time of things, making only 12 unforced errors while Venus had 33. Every match was intimidating, but you go out and do the best you can. I will not put pressure on myself. As I always say, we have to have these uncomfortable conversations so we can start just fighting for having equality throughout'. Just that it is going to be a huge challenge for me.
"I honestly would love to face the world No. 1", said Williams.
Serena Williams is used to dominating her competition at the Australian Open, but showed once again she was a magnanimous victor when she took the time to console her Ukrainian opponent who became overwhelmed after suffering a heavy defeat.
Women's 4th round: Danielle Collins beat No. 2 Angelique Kerber 6-0, 6-2; No. 8 Petra Kvitova beat Amanda Anisimova 6-2, 6-1; No. 15 Ash Barty beat No. 30 Maria Sharapova 4-6, 6-1, 6-4; Anastasia Pavlyuchenkova beat No. 5 Sloane Stephens 6-7 (3), 6-3, 6-3.
She left the court lifted by Williams' words.
Unlike any of Serena's foes until now, Halep has won a major title, last year's French Open. She is nearly unique in her style.
Yastremska rolled her right ankle midway through the match and took a medical time-out to have her foot bandaged when trailing 4-1 in the second set. Her quality of the shots.
While Nishikori beat Pablo Carreño Busta 6-7, 7-6, 6-4, 7-6, Pouille upset Borna Ćorić 6-7, 6-4, 7-5, 7-6.
While the generational divide between Williams and Yastremska and Anisimova is enormous, the all-time great has clearly not forgotten from where she came. Everyone else she faced early were cannon fodder - Karolina Pliskova in New York, Julia Goerges at Wimbledon being the highest seeds she overcame.
"Completely unnecessary to turn on the lights", he said in roasting the organizers. "Maybe I'm wrong, maybe not", Djokovic told reporters.
"I am confident that I am in this position".