But even Halep's supreme defensive game wasn't enough to stop Williams, who managed to find another gear after saving three break points down 3-2 in the deciding set.
Osaka plays Svitolina in the other quarter-final on that side of the draw and on Monday she defied her own history when, for the second time in a row, she lost the first set but still went through, beating 12th seed Anastasija Sevastova 4-6, 6-3, 6-4 in an hour and 47 minutes on Laver.
"She's the number one player in the world and there's a reason why..."
The 37-year-old American beat the Romanian top seed 6-1, 4-6, 6-4 in an epic three-setter to line up a last eight clash with Czech eighth seed Karolina Pliskova.
When the game was tied at 4-4, Williams started to commit more unforced errors with Halep brilliantly rising to the occasion breaking the American to win the second set 6-4.
"It was an intense match and there were some incredible points, but I love being here", she said. The first Grand Slam of 2019 sees world number one Novak Djokovic aiming for his third consecutive slam title, and seventh Australian Open.
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'I'm such a fighter I just never give up. "There's definitely something that's innate".
"I love playing tennis, I love being out here, I love this court".
Williams who won the 2017 Australian Open while pregnant with her daughter, resumed her professional career a year ago and immediately reached the finals of two Grand Slams (Wimbledon and US Open) during her first season since returning from maternity leave.
Williams had given up only nine games in her three previous games - a first-week strike rate she hasn't matched in a major since the 2013 US Open - but she had to step up in class from the likes of Dayana Yastramenska and Eugenie Bouchard.
Halep broke again to take a set off Williams, celebrating with a fired-up double fist pump.
"But she can also miss".