Men's singles second round
Australia’s Kokkinakis was on the brink of a Melbourne Park breakthrough, a game away from his first appearance in the Australian Open third round.
But Murray, for years having battled to regain the form and heights that defined his career prior to hip surgeries, would not concede.
Despite being just two points from defeat, twice, in a compelling third set, he wrested it from Kokkinakis with a steadier display of tennis.
He survived five break points in a 70-minute fourth set, eventually slotting an ace to send the match to a fifth.
And once there, he outcompeted an opponent almost 10 years his junior.
After five hours and 45 minutes at Margaret Court Arena – the longest match of his career – Murray emerged an unlikely 4-6 6-7(4) 7-6(5) 6-3 7-5 winner.
"I don't know. It was unbelievable that I managed to turn that round," said Murray, who next faces 24th seed Roberto Bautista Agut in what is his deepest AO run in six years.
"Thanasi was playing, I mean, serving unbelievable, hitting his forehand huge and I don't know how I managed to get through it.
"I did start playing better as the match went on. And yeah, I have a big heart.
"I think now I'm outright the most matches coming back from two sets to love down. So I have done it before, I have experience of it, and I just rely on that experience and that drive and that fight, and my love of the game, and competing, and my respect for this event, and the competition.
"That's why I kept going."
Extraordinarily, Murray had already played a five-set thriller at Melbourne Park this year.
In round one, he saved a match point in an upset win over 13th seed Matteo Berrettini – his first victory over a top-20 player at a Grand Slam tournament since 2017.
Kokkinakis was among the many observers who was thrilled with the 35-year-old’s triumph.
He understood the many physical challenges that Murray had endured – including resurfacing surgery and a metal hip – since he contested the fifth of his Australian Open finals in 2016.
But Kokkinakis had, of course, battled his own physical challenges – including major shoulder surgeries, as well as back, knee and ankle injuries, then serious illness – throughout his career.
A straight-sets win over Fabio Fognini in the AO 2023 first round (played over a 24-hour period after heat and rain delays) underlined that the world No.159 was now in peak fitness.
In a second career meeting with Murray, a steelier mindset from Kokkinakis would also count.
With early nerves settled, Kokkinakis was soon dictating and a series of showstopping forehand winners set the scene for the following few hours.
He gained a critical first service break as dictated in the seventh game, and with aggressive intensity, Kokkinakis maintained the lead to take the first set.
With his winner count growing, the Australian was also the aggressor throughout the second set.
But in the first signs of the troubles he would have closing out leads, tension factored into the Australian’s game; with Murray saving two set points before a third was surrendered on a Kokkinakis double fault.
A subsequent tiebreak provided the opportunity to reset, with a stunning second serve ace featuring as he took a 5-2 lead.
Two more set points passed by for Kokkinakis, before he at last claimed a two-set advantage with his 12th ace.
In the third set, Kokkinakis broke Murray twice and surged to a 5-2 lead.
But just like in the second set, he had trouble closing it out, broken as he served for the match at 5-3.
And this time, Murray made him pay for that missed opportunity.
Murray underlined his champion credentials as he claimed the crucial break back, and the Australian was clearly in danger as a tiebreak followed.
Murray found some attacking winners, and as the local time edged past 1.30am, Kokkinakis’ concentration faltered – and he shanked an overhead to hand Murray the third set.
In an increasingly energy-sapping contest – the first two games of the fourth set took 27 minutes to complete – Kokkinakis became dispirited.
His mood was not helped when he rolled his ankle at the end of the fifth game.
The sizeable crowd who remained roared, sensing the increasing drama, and showing their appreciation for the contest.
Murray showed his appreciation for them, and his level increased, with the Scot barely committing unforced errors and playing a greater percentage of shots inside the baseline.
He staved off two break points in the ninth game, and forced a fifth – which was similarly unforgettable.
Kokkinakis found himself deep in a fifth set, the time beyond 3.30am, staring down three break points. But he erased them with winners, fended off a fourth, miraculously held for 4-3, and turned the set back in his favour.
And again, he came within two points of victory, in the 10th game.
But Murray held, broke serve after yet another dramatic game – he required four break points – and was able to serve his way into the third round.
One last backhand winner ended the contest.