The Spanish world Number 1 took just 1hr 50min to reach the fourth round with a 6-1, 6-3, 6-1 demolition of the 28th seeded Bosnian on Margaret Court Arena whereas Grigor Dimitrov and Elina Svitolina kept their Grand Slam hopes alive on a hot draining day."I was very, very focused, i'm very happy with everything and to have another chance on Sunday." Nadal said.
That chance will be against 24th seeded Argentine Diego Schwartzman for a place in the quarter-finals.
Third seed Dimitrov, who could meet Nadal in the semis, had plenty to prove after a huge second-round fright from a qualifier, who pushed him to five sets.
And the Bulgarian delivered in a testing 6-3, 4-6, 6-4, 6-4 win over Russian rising star Andrey Rublev as temperatures touched 40 Celsius. “These are the most important matches for me, when things are not working for me and I find a way," he said. "I'm feeling good physically, the heat didn't scare me at all today, so that's a good sign."
He will next face the winner of an intriguing night match which pits Australian Nick Kyrgios against French veteran Jo-Wilfried Tsonga.
Fourth seed Svitolina also kept her title dreams alive by ending the hopes of young teenage pretender Marta Kostyuk.
At just 15, Kostyuk was the youngest Melbourne Park third-round contestant since Martina Hingis in 1996, and was hailed after her previous win as "the future of tennis".
But she still has a lot to learn with fellow Ukrainian Svitolina handing out a 6-2, 6-2 lesson."She's definitely got a bright future," said Svitolina, adding: "It's very special for me to get past the third round."
She next plays another qualifier — big-serving Czech Denisa Allertova who romped past Magda Linette 6-1, 6-4 — for a place in the quarter-finals on Sunday.
Cornet was among players wilting in the heat, with a doctor taking her blood pressure early in the second set as she succumbed to the baking weather.
No matches have been called off or roofs closed at the opening Grand Slam of the year despite the soaring temperatures, with tournament organiser Craig Tiley defending the decision. "These are professional athletes, we are at the end of the day an outdoor event. We want it to stay an outdoor event as long as possible but at the same time ensuring that the health and wellbeing of players is taken care of." He said.
Organisers only activate the extreme heat policy when the temperature exceeds 40 Celsius and the wet bulb globe temperature index hits 32.5 Celsius.
On Thursday, Novak Djokovic described the conditions as "brutal", complaining it was hard to breathe.
Kyle Edmund joined Nadal in the round of 16, overcoming the elements in a fighting five-set win over Nikoloz Basilashvili and will next play Italian Andreas Seppi who won a battle of the veterans against Croatia's 38-year-old Ivo Karlovic.
Spanish 10th seed Pablo Carreno Busta, a semi-finalist at last year's US Open, also marched on.
Despite being the second seed, Caroline Wozniacki has not impressed so far.
She is the late match on Rod Laver Arena against Dutch 30th seed Kiki Bertens and will play 19th-seeded Slovak Magdalena Rybarikova if she wins.
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