MELBOURNE, Australia - World No.1 Simona Halep hung on by a nail (or two?) to win one of the best and longest matches of the 2018 Australian Open, outlasting an inspired Lauren Davis, 4-6, 6-4, 15-13 to reach the fourth round in front of an enthralled Rod Laver Arena.

"I gave everything I had today, and actually, I'm really proud that I could stay there and win it," Halep said in her post-match press conference. "It was not easy at all. She played great."

Struggling with an ankle injury since her first round against Destanee Aiava, Halep recovered from a set down and saved three match points in a row in the 22nd game of the deciding set, running nearly three miles throughout.

It was the first time Halep, who said she was "almost dead" in her on-court interview, had come from triple match point down to win.

"Many first times today," Halep said in press, when told about that fact. "I'm really, really proud of that, and I'll just say that this match meant a lot for me. Doesn't matter what is gonna happen now. I say that it's a big win in many ways, and I'll take it."

Unseeded but ranked as high as No.26 last spring, Davis captured hearts and minds with her fearless play, battling back from 3-1 in the third and thrice breaking the Romanian as she served for the match.

"I'm very tired," Davis said in her post-match press conference. "But, I mean, there is a lot to take away from that match. I played really, really well. Left all that I had out there on the court, and I did all that I could do. I think there is quite a few positives to take away from and to learn from, so things are looking up."

Halep amped up her aggression when her back was against the wall, and maintained the pressure even as Davis began losing toenails - one in between her second and third match points - ultimately serving out her spot in the second week.

"It was definitely unfortunate, the timing of it," said Davis. "I think my second toes are just a bit infected. I was just jamming them a lot with how much I was moving around the court."

"That first match point just, I felt something and I couldn't really put any pressure -- it was my right toe, and then it eventually was my left toe, also. The trainer wrapped them really well and I was able to move fine after that."

Halep complimented Davis in press. "She was moving really well and her backhand short-cross was amazing. I didn't have reactions for those shots, but still I thought my backhand is strong enough to go there and to hit some down-the-lines."

"She was very aggressive," Halep continued. "She defends very well, and she also comes to the net. She's a great player. Today she played amazing."

The three hour, 44 minute epic was the third longest in Australian Open history. Clocking in at 48 games, it ties the 1996 quarterfinal classic between Chanda Rubin and Arantxa Sanchez Vicario.

Halep will next take on Japan's Naomi Osaka, who was the winner of a young gun face-off with hometown hero and No.18 seed Ashleigh Barty, 6-4, 6-2.

"Osaka is hitting strong, so strong," said Halep in her post-match press conference. "I have to be strong, if I can, on my legs, and just stay there, playing fast, opening the court, as I do all the time."

"For sure it's a tough match. I'm not thinking the result. I just want to get ready to play with my legs."