A potential concern for Djokovic, who next plays second seed Alexander Zverev in what will be his 50th slam semi-final, is a left leg problem that required treatment during the opening set, but he seemed to improve physically as the match went on.

Alcaraz trailed 3-4 in the head-to-head and had lost their last meeting in the Olympic final, but he felt like a solid favourite on age, form and having defeated his rival in back-to-back Wimbledon deciders.

He had never beaten Djokovic on hard courts, though, nor made it past the quarter-finals here, and the 37-year-old used all his experience of successful nights past on Rod Laver Arena to befuddle Alcaraz.

Coach Andy Murray, sat in the courtside box, also deserves credit because this was a tactical triumph as Djokovic blunted the firepower and spirit of his opponent before the 21-year-old rallied in a spectacular denouement.

It took both men a bit of time to settle into the contest in cool, windy conditions.

Despite one incredible volley winner, Alcaraz dropped serve in the second game amid a slew of errors, only to break straight back, striking a backhand winner down the line.

The contest then ticked along routinely until the ninth game when, after a long rally at 15-15, Djokovic crouched down wincing and gave a little shake of the head towards his box.

He managed to save two break points but not a third and swiftly headed off court for a medical timeout.

He returned with strapping visible on his left thigh and Alcaraz served out the set, but Djokovic showed positive signs early in the second, taking the fight to his young opponent and opening up a 3-0 lead.

It was a scrappy contest, with some moments of brilliance from both men but errors aplenty, and back came Alcaraz to level the match as Djokovic limped around the court.

But the Serbian has won the title here on more than one occasion despite being physically compromised and he produced a superb returning game to break serve again and take the set.

Djokovic had found a real groove on his ground strokes and particularly on return, piling the pressure on an increasingly frustrated Alcaraz.

He cracked at 2-3 only to hit straight back, but the Spaniard was shouting at himself again as Djokovic clinched a third straight break, sending a forehand arrowing into the corner and then putting his finger to his ear as he soaked up the cheers.

The 37-year-old had stayed supremely calm but he conducted his orchestra once more after coming from 0-30 down to clinch the set.

Alcaraz looked out of ideas and another break early in the fourth pushed him closer to the exit, but, on the ropes, the Spaniard punched back.

A pulsating 33-shot rally that left both men barely able to stand helped him save virtual match point at 2-4 15-40, but Alcaraz could not break the Djokovic serve and the 37-year-old roared in delight after a final backhand from the Spaniard hit the net.

Earlier, Zverev reached his third Australian Open semi-final with a four-set win over American Tommy Paul.

The second seed, who is bidding for a first grand slam title, had lost both his previous two meetings against Paul but proved the stronger in the big moments to win 7-6 (1) 7-6 (0) 2-6 6-1.

Paul, seeded 12th, served for both the first and second sets, but Zverev broke back on each occasion and played two excellent tie-breaks.

“I feel like I stole both of those sets in a way, because he was playing better than me,” said Zverev.

“In the tie-break I played quite well. He maybe missed a little bit more than he should have. I’m happy that I won in four sets because this was a difficult one.”