The Australian Open top seed hailed the "new Simona" Halep after saving three match points for the first time in her career to survive an epic 15-13 in the third set on Saturday.
Courageous unseeded American Lauren Davis lost a middle toenail on her left foot and had to be treated twice by the physio as she threw everything at Halep in a third set that alone lasted 2hr 22min.
The Romanian eventually won the marathon third-round clash 4-6, 6-4, 15-13 in 3hr 44min after three times stumbling when serving for the match.
And she credited a new-found calmness for getting her through the toughest test of her career at 10-11, 0-40 in the third set.
"I'm just trying to change myself to not think that much about the points," Halep said. "It's really tough when the opponent has match point," adding that her reputation for losing her temper and folding in pressure moments of important matches was a thing of the past.
"If we compare the old Simona with the new Simona... I was a little bit stronger in that moment, for sure," said the world No 1.
"You just go there and hit like without thinking. I did that, and I think she was a little bit tired at that moment. The pressure was on, also, and I was a little bit stronger in that moment, for sure."
Halep, suffering from ankle problems, came under constant pressure as the world number 75 hit 52 winners to all parts of the court. But when she finally managed to serve out at the fourth time of asking it brought a standing ovation from Rod Laver Arena.
"I never played a third set so long. I'm almost dead," the Romanian said after finally edging across the finish line. "My muscles are gone. I don't feel my ankle any more."
Halep nows plays either 18th seed Ashleigh Barty of Australia or Japan's Naomi Osaka in the last 16 after the longest match of the women's tournament so far.
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It eclipsed the 3hr 1min that fellow Romanian Irina-Camelia Begu took to defeat Ekaterina Makarova of Russia 3-6, 6-4, 8-6 in the first round on Monday.
But it was an hour short of the 2011 Australian Open record set as Francesca Schiavone of Italy beat Russia's Svetlana Kuznetsova 6-4, 1-6, 16-14 in 4hr 44min.
Halep said that she now had nothing to lose for the rest of the tournament because "honestly, I thought it's over at that moment [three match points down]. But it was good because I relaxed my arm and I served pretty well those three points.
"Doesn't matter what is going to happen now," Halep said. "I say that it's a big win in many ways, and I take it."
