Simona Halep makes a backhand return against Lauren Davis during their marathon third-round clash at the Australian Open on Saturday. Photo: Vincent Thian/AP

MELBOURNE – World number one Simona Halep saved three match points to survive a titanic struggle and make the last-16 at the Australian Open on Saturday where she joined Karolina Pliskova and Caroline Garcia.

With the temperatures a manageable 26 degrees Celsius at Melbourne Park after two days of oven-like conditions, the Romanian looked out for the count against American Lauren Davis.

But she finally got over the line 4-6 6-4 15-13 in a gruelling three hours and 44 minutes on Rod Laver Arena to make the fourth round in a contest that took its toll.

“I’m almost dead,” the tenacious Romanian said after the incredible battle, in which Davis lost a toenail and Halep served for the match four times.

“The feeling in my muscles is gone, and I don’t feel my ankle anymore,” she added.

Davis is ranked just 76 in the world and was knocked out in the first round of all four Grand Slams last year, but you would never have known it.

Halep, a former quarter-finalist at Melbourne Park who slumped out in the first round last year, will next play Australian Ashleigh Barty or Japan’s Naomi Osaka in her quest for a maiden Grand Slam title.

Sixth seed Pliskova also had a tough test, beating fellow Czech Lucie Safarova 7-6(6) 7-5.

In contrast, US Open finalist Madison Keys was in fine touch as she benefits from the guidance of former great Lindsay Davenport.

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.

“Lindsay is amazing. We’ve had three years together and she has taught me how to handle big moments like this,” said Keys, who made the Australian Open semis in 2015.

She will next test herself against French eighth seed Garcia, who was too strong for Belarussian Alaksandra Sasnovich, winning in three sets.

“I haven’t done too well against her before and I want to improve,” Garcia said of Keys.