“It feels surreal, to be honest,” said Djokovic, who had lost the five previous matches to the 24-year-old Italian Sinner.
He added: “I have tremendous respect for him, an incredible player. He pushes you to the very limit, which is what he did tonight to me.”
With age and injuries catching up with Djokovic, Sunday may represent the Serbian’s best chance of seizing that elusive 25th major, although his gritty display against Sinner shows he still has plenty left in the tank.
His last Grand Slam title came at the US Open in 2023, since when Alcaraz and Sinner have dominated men’s tennis.
It has left Djokovic stranded alongside Australia’s Margaret Court – who was in the stadium watching – tied on 24 majors.
A defiant Djokovic said people writing him off had fired him up.
“I never stopped doubting. I never stopped believing in myself,” said the former world No 1, seeded fourth.
“There’s a lot of people that doubt me. I see there is a lot of experts all of a sudden that wanted to retire me or have retired me many times the last couple of years.
“I want to thank them all because they gave me strength. They gave me motivation to prove them wrong, which I have tonight.”
Asked by reporters where he rated his display, Djokovic said: “For sure, one of the best performances in the last decade or so.”
Sinner made a rapid start at Rod Laver Arena, breaking Djokovic’s serve to race into a 3-0 lead.
The four-time major winner was in superb touch, his serve firing and his groundstrokes unerring to seal the first set.
Back came Djokovic, breaking serve for a 3-1 lead in the second set and then saving three break points for 4-1.
Djokovic sent a whipping cross-court forehand beyond Sinner on his first set point to level the match.
Djokovic seemed to wilt midway through the third set, holding his chest briefly and then half-collapsing into his seat.
Sinner had three break points at 5-4 and nailed the set on the second one when a Djokovic lob drifted long.
But the gutsy Djokovic was not done, breaking the Sinner serve early in the fourth set as the time ticked past midnight.
They went to a deciding fifth set, and the tension went up another notch, as Sinner repeatedly squandered chances to break serve.
Djokovic was ruthless, seizing the break for 4-3, then holding, to put an 11th Melbourne final within reach.
Somehow Sinner saved two match points at 4-5 down, before Djokovic got the job done third time lucky.
Djokovic is the undisputed king of Melbourne Park, having won 10 titles there.
But he admitted he was lucky after reaching the semi-finals and acknowledged he was the underdog against Sinner.
Djokovic was two sets down in his quarter-final to Lorenzo Musetti when the Italian fifth seed retired hurt.
He also had a free ride through the fourth round when Jakub Mensik pulled out injured.
Djokovic reached the semi-finals of all four majors last year, but failed to go further.
