The American, particularly brilliant off the backhand side whose average speed appears higher than the highest registered in the men's singles draw, forced the world No.1 to an exhausting 3 hours 45 minutes battle, ten years to the day since Hewitt and Baghdatis ended a memorable match at 4.30 am.
Halep, still nursing the ankle she injured her ankle in her first-round win, said: "I'm nearly dead".
"I never played a third set so long". Solid groundstrokes saw her claim a break point chance, but a fortunate net cord victor saved Halep from the brink and got her onto the scoreboard.
"It's a good position for me to be in and I'm enjoying it". Added Halep of the three match points she faced: "You just go there and hit like without thinking".
"But it was nice to win this match, to be on this court and to be in the fourth round of this tournament". "I just looking from match to match, day by day", said Kerber when asked about being the only major victor left in the draw.
Class prevailed, with Halep taking the second set 6-4. Neither has an imposing serve - four aces and two service winners between them in 303 points - and so breaks were numerous (nine in the third set itself) and miles had to be run. "I really do believe that I can otherwise I wouldn't be here", said the five-time Grand Slam champion after losing 1-6, 6-3 in 64 minutes.
Primark enjoys "record Christmas" beating expectations
Shares in the group, majority owned by the family of Chief Executive George Weston, were down 3 percent at 0945 GMT. However, most analysts regard Primark as well positioned to withstand the pressure on discretionary spending.
With the temperatures a manageable 26 Celsius (79 Farenheit) at Melbourne Park after two days of oven-like conditions, the Romanian looked out for the count against American Lauren Davis. She took a medical timeout after failing to take advantage of the three match points and before serving at 11-11, and then when leading 13-12 before Halep served. Davis saved five break points in the 23rd game but she looking increasingly suffering.
Halep finally served out the match at the fourth attempt to move to the next round of the tournament. Dropping her third round match to Anett Kontaveit, she does at least tie her best career performance so far at the major tournament.
It's, beyond any doubts, a Darren Cahill win as well, who gave the Romanian to stand still and win a match that a couple of seasons ago she would have lost.
Flying under the radar, the 17th seed has surrendered just 16 games on her way to the fourth round after beating Romania's Ana Bogdan 6-3, 6-4.
Maria Sharapova says she is inspired by the likes of thirtysomethings Serena Williams and Roger Federer to get back to the top after her doping ban. "I mean, I got to the point where I was so exhausted where I just told myself to swing and move, and, I mean, for the most part it was very effective. After this match I think tomorrow is gonna be worse, but I just push, push myself, and we will see what's gonna happen".