At the end of another breathless exchange in the early stages of the most highly anticipated match of the Australian Open, alone in the centre of the colossal Rod Laver Arena, Novak Djokovic squatted down on to the court before solemnly stretching his lower body.

In the previous 30 seconds, Djokovic had been run ragged by a Carlos Alcaraz in full flight; he was ruthlessly dragged from sideline to sideline by the Spaniard’s nuclear groundstrokes, pulled forward by a delicate drop shot and then vanquished by a laser-like forehand winner as he stood helplessly at the net. Djokovic pulled up from the gruelling point limping and he called for the physio.

It seemed for a few fleeting moments that the challenge of holding off one of the most special young players in history might be beyond Djokovic and his worn-down 37-year-old body. Instead, he responded with a masterpiece of a performance in the tournament that has defined his career, offering yet another reminder of his greatness by rallying from a set down to defeat Alcaraz 4-6, 6-4, 6-3, 6-4.

Djokovic has now reached 50 grand-slam semi-finals, extending his all-time record. As he continues to rewrite all the age-based records in his name – he is now the third man to reach multiple grand slam semi-finals after turning 37 and he is also the third man in the Open era to reach the semi-finals at this age. Ken Rosewall and Roger Federer are the others to achieve this distinction.

In his 12th Australian Open semi-final Djokovic, the seventh seed, will face the third seed, Alexander Zverev, who defeated the 12th seed, Tommy Paul, 7-6 (1), 7-6 (0), 2-6, 6-1.

With 16 years separating Djokovic and Alcaraz, their contests over the past two years have illustrated the changing complexions of their careers. While their first meeting occurred when Djokovic was No 1 and Alcaraz had only just broken into the top 10, Alcaraz is now an established four-time grand-slam champion and, as the third seed, this was his section of the draw. Djokovic entered the match a clear challenger and underdog as he tried hard to hold off Alcaraz.

Carlos Alcaraz tries to get to a lob during his match against Novak Djokovic. Photograph: Lukas Coch/AAP

The last time they met, Djokovic provided perhaps the most spectacular illustration of his mental strength and desire in his career as he willed himself to the Olympic gold medal in Paris in two incredibly tight sets. Outperforming the new generation over the best of five sets format at the grand slams, however, becomes more difficult each year.

In the strong winds on a cool night , the conditions did not stop the players from trading blows with immaculate depth and intensity from early on. After a slow start, though, it was Alcaraz who dictated and decided most exchanges in the first set with his forehand and determination to close down the net.

At 4-4 on Djokovic’s serve, the Serb pulled up badly at the end of a gruelling rally. After stretching out his lower body, Djokovic spent the rest of the game limping and he took an off-court medical timeout after conceding the break. Once the match restarted, Alcaraz coolly served out the set.

His left thigh bandaged tightly, Djokovic spent much of the second set limping between points, wincing after sharp movements and he appeared to be in genuine pain. But he also played with astonishing focus and commitment, forcing himself inside the baseline and playing fearless attacking tennis as he pounded his forehand without hesitation. Even as Alcaraz retrieved his early break, testing Djokovic’s movement with ample drop shots and sustained aggression, Djokovic maintained his composure. He made his move at 5-4 on Alcaraz’s serve, ending an immaculate return game with a searing backhand return winner to level the match.

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In his discomfort, Djokovic presented the sharpest version of himself. He was relentless, deflecting almost every return with consistency and depth, pinning Alcaraz in his backhand corner and finding the answer to so many of the long exchanges with his forehand aggression. Alcaraz, meanwhile, was too passive and flat, unable to strike the ball with unrelenting freedom and aggression.

Andy Murray, coach of Novak Djokovic, applauds his efforts against Carlos Alcaraz. Photograph: Francis Mascarenhas/Reuters

But Alcaraz fought to the bitter end. Down a break point at 2-4, he somehow pulled himself through an utterly brutal 33-stroke rally that left both players hunched over in exhaustion. After holding serve, Alcaraz used the desperate encouragement from the delirious crowd to generate two break points. But Djokovic was not to be denied as he sealed another supreme achievement in a 20-year grand slam career filled with them.

After closing out a monumental victory with a steely hold, Djokovic shared a warm, pointed embrace with his new coach, Andy Murray. It was precisely for these moments, the biggest matches against the best players, that Djokovic enlisted his old rival to his cause.

This was a reflection of his enduring commitment to his craft and the incredible level he continues to compete at so deep in his career, but also of the work they have produced in a short amount of time. As he chases down his 25th grand slam title, it has only just begun.