Halep saved three match points at 10-11 0-40, but recovered to hold before securing a break in game 27, eventually getting across the line after three hours and 45 minutes of gripping action.
IT WAS NEARLY "Bye, Simona" but the top seed showed the knack of a world No 1 to claim an incredible victory.
A premier match this weekend features former champions Angelique Kerber and Maria Sharapova.
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.
"It definitely was a very tough match".
With the temperatures a manageable 26 Celsius (79 Farenheit) at Melbourne Park after two days of oven-like conditions, the Russian was no match for the German, flopping 6-1, 6-3 in a battle of the former champions.
World number one Simona Halep survived a titanic tussle with America's Lauren Davis to reach the Australian Open fourth round - fighting back from a set down and saving three match points in a classic that stretched towards the four-hour mark.
Halep finally served out the match at the fourth attempt to move to the next round of the tournament. "I never played the third set so long".
Halep, a former quarter-finalist at Melbourne Park who slumped out in the first round a year ago, will next play Australian Ashleigh Barty or Japan's Naomi Osaka in her quest for a maiden Grand Slam title.
The women's draw has already lost Garbiñe Muguruza, the No. 3 seed and the defending Wimbledon champion; Venus Williams, the No. 5 seed who was the runner-up here previous year; and Jelena Ostapenko, the No. 7 seed and the defending French Open champ. Unexpectedly, the American regained her composure and found her groove once more, grabbing back the break by prevailing in a marathon rally.
"I'm here because I'm motivated to get better at my craft".
Davis and Halep meets at the net for the handshake after the incredible match
'I'm very exhausted, ' Davis said.
Roger Federer has arguably the most handsome single-handed backhands in tennis.
"But, why not?" asked Jim Courier on court after the Swiss trounced Richard Gasquet in straight sets.
"I mean, every point was just super long".
On Courier's request, Federer also performed the 'smoldering intensity' on court.
Davis made a decision to take a different approach coming into this Australian Open. "Don't know if (winning) is going to happen this year, but so far, so good". It happened in NY.
Halep's gained some revenge from the last - and only - time the pair met in a Grand Slam tournament.
"I'm gluten-free. They don't have a gluten-free pasta".
Halep admitted after the match that she still was "not 100 percent" and that the ankle remains a concern.
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