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Top-ranked Carlos Alcaraz was imperious against Denis Shapovalov in the night session, blasting past the Canadian 6-1, 6-4, 6-2 to book a meeting with Lorenzo Musetti.
Djokovic's coach Goran Ivanisevic said after the final that the world No. 1 battled the injury, which would have forced most players to quit.
The Serb also equalled Rafael Nadal's record of 22 Grand Slam singles titles with the win.
Nine-time champion Djokovic will meet third seed Stefanos Tsitsipas in Sunday's decider after the Greek booked his first final at Melbourne Park by beating Russian Karen Khachanov.
Khachanov reached the semifinals after ailing American Sebastian Korda retired while trailing 7-6(5), 6-3, 3-0.
A year after dumping Sinner out in the quarters at Melbourne Park, third seed Tsitsipas crushed the Italian's hopes of a great escape.
Tsitsipas will next take on Italian Jannik Sinner in what could be a tricky test.
Frances Tiafoe sealed the title for Team World with victory over Stefanos Tsitsipas.
Tsitsipas was knocked out by Colombian qualifier Daniel Galan, who clinched the 6-0 6-1 3-6 7-5 win on his ninth match point.
Coric signalled his return to full fitness from shoulder surgery and showed that he will be a threat at the US Open.