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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.
An 11th straight win of the year also means the Belarusian will return to a career-high ranking of number two behind Iga Swiatek, reaping the rewards of her improved mental stability and service to emerge as a genuine threat in big tournaments.
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.
Sabalenka surged into the final with a 7-6(1), 6-2 win over unseeded Pole Magda Linette to extend her unbeaten start to the year.
The former No. 1 set up a last-four meeting with American Tommy Paul.
The unseeded Indian pair knocked out third seeds Desirae Krawczyk and Neal Skupski 7-6(5), 6-7(5), 10-6 in the semifinal that lasted one hour and 52 minutes.
Sabalenka, the only top-10 seed left in the draw, took her chances in a physical one-hour first set littered with break points before running away with the second.
Khachanov reached the semifinals after ailing American Sebastian Korda retired while trailing 7-6(5), 6-3, 3-0.
Azarenka rolled back the years as the two-time champion crushed third seed Jessica Pegula 6-4, 6-1.