The game looked bleak for Venus as Halep claimed a third successive break to open the second set.
Persistence paid off when Halep converted her fourth break opportunity, darting forward to crack a backhand beyond Williams' reach.
Top seed Simona Halep had the odds stacked against her ahead of the Australian Open but the Romanian proved her title credentials with a breezy 6-2 6-3 third-round win over multiple Grand Slam victor Venus Williams on Saturday.
Halep, who is returning from a herniated disc, has limped through her first two matches at Melbourne Park, taken to three sets in both, and knows she will need to up her game to make the last 16. "I don't feel like I'm there yet", she said. "I liked that. It showed that she wasn't just there to play the match, she was there to win".
Williams said later in her post-match press conference seeing her opponent in distress "broke my heart" and she recalled being in Yastremska's position when losing to Venus in the 2000 Wimbledon semifinals. I have to move her and give my best. "It's good to see that attitude".
In the second round, Halep needed two hours and 31 minutes to survive another baseline dog fight against American youngster Sofia Kenin and win in three sets.
The 37-year-old continued her impressive passage through the draw with an emphatic 6-2 6-1 victory over the 18-year-old Ukrainian, who was not born when Williams won her first Grand Slam singles title in 1999. Simona Halep lost last year's Final and has to overcome the biggest challenge of all to try and get back there. She's been a lot at number one.
That said, this is going to be a much better test of the American great's level than anything she's encountered so far. "I couldn't help it. Young girls, young women, just want to go out there and do their best and want to win". At least their last meeting was competitive - a three-sets win for Williams in the 2016 US Open quarter-final. "For me that's like, one of the biggest things I always thought I could improve, because it sort of seems like before I would accept defeat in a way, and then this time I just wanted to learn from the last match that I played in Brisbane", she added, referring to a straight-set loss to Ukraine's Lesia Tsurenko.
Williams swatted aside Ukrainian teenager Dayana Yastremska 6-2, 6-1 in a Melbourne Park mauling that reduced the world number 57 to tears.
"I think I'm getting there", came the reply.
"Yeah, it will be great".
The Romanian said: "In my opinion, to be number one in the world and to be the best player in the world, it's a little bit different. So, yeah, it will be good".
"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. She's been to three other Grand Slam finals, including a year ago at the Australian Open.