World No.1 Simona Halep has emerged from a titanic third-round scare from Lauren Davis to progress to the second week of the Australian Open - and a potential meeting with top Aussie Ashleigh Barty.

Halep, playing through an ankle concern, dropped the first set before fighting back to defeat the world No.76 4-6 6-4 15-13 across three hours and 44 minutes on Saturday in the match of the tournament so far.

The Romanian saved three match points at 11-10 in deciding set of the classic, overcoming Davis after the unseeded American lost a toenail in the marathon third set.

"I'm almost dead," Halep said in an on-court interview.

"I feel that my muscles are gone. My ankle, I don't know how it is because I don't feel it any more.

"I've never played a third set so long. I'm very happy I could stay and win it ... it was very nice we could show such good tennis."

The match had everything.

Davis showed her intent with a barnstorming first set, unleashing her powerful backhand to the delight of the Rod Laver Arena crowd.

Halep responded in the second set, showing the consistency that's made her world No.1 - hitting just two unforced errors.

The third was simply out of this world.

The 142-minute decider lasted longer than all but six matches so far in the tournament, pushing the match out to tie Chanda Rubin's 1996 quarter-final win over Arantxa Sanchez Vicario for most number of games in a women's singles match at Melbourne Park.

Incredibly, Halep served for the set four times but didn't hold a match point until the very last point.

Each time, Davis jumped off the deck to break back, fist-pumping to an appreciative crowd.

The American smashed 52 winners but will look back and wince at the missed opportunities to make a first fourth-round appearance at a grand slam.
The match points were lost with groundstrokes that crept the wrong side of the baseline, and a booming Halep serve and fearless forehand winner.

Davis was forced to treat her injured toe shortly after at 11-11, wincing with pain as Halep looked on po-faced.

Davis wouldn't win another game after a second medical time-out at 13-12.

Instead, it was Halep who progressed to face the winner of Barty's clash with Naomi Osaka, played later on Saturday.

That's if she can walk.

"You sit through one of those matches once in every 10 years ... it's never happened to me as a coach," Halep's Australian coach Darren Cahill told Channel Seven.

"There's a lot of Voltaren and painkillers in her system.

"We'll have to really rehab ... it's a little bit of the unknown. I'm pretty sure she hasn't played a match like that before.

"But the fact she's out there playing with a little bit of a dodgy ankle ... she's a tough chick."