The world No.1 received a controversial medical time-out deep in the third set before recovering to outlast and "exhausted" Zverev 6-4 7-6 (7-5) 6-7 (3-7) 6-7 (4-7) 7-5 in a five-hour, 27-minute classic at Melbourne Park on Friday.
Alcaraz looked headed for the exit gates when Zverev served for the match at 5-4 in the fifth set before the indomitable Spaniard dug deep to deny the German third seed a second straight Open final spot.
"Believing. Believing all the time," Alcaraz said.
"I always say that you have to believe in yourself no matter what, no matter what you're struggling, what you've been through.
"No matter anything, you've still got to believe in yourself all the time.
"I was struggling in the middle of the third set. Physically, it was one of the most demanding matches that I have ever played in my short career, I would say.
"But I've been in these kind of situations. I've been in these kind of matches before, so I knew what I had to do," Alcaraz added.
"I had to put my heart into the match. I think I did it. I fought until the last ball.
"I knew that I was going to have my chances."
The tension-filled victory edged the 22-year-old sensation to within one tantalising win of completing a fabled career grand slam.
Even if he loses his maiden Open final on Sunday night to inspired 10-time Open king Novak Djokovic, Alcaraz has already etched his place in the sport's history books.
The smiling assassin joins Sinner, Djokovic, countryman Rafael Nadal, Roger Federer, Andre Agassi and Rod Laver as only the seventh man in the 58-year professional era to reach consecutive finals of all four grand slams.
But the reigning French and US Open champion will likely not be content unless he captures a first AO crown and surpasses American Don Budge as the youngest player to win all four majors.
Adding an extra edge to the blockbuster, Djokovic will also be chasing immortality after the 38-year-old marvel wound back the clock to end Sinner's two-year title reign with an extraordinary 3-6 6-4 4-6 6-4 6-4 victory in the equally remarkable four-hour, nine-minute second semi-final.
In snapping a run of five straight losses to Sinner, Djokovic also denied the Italian world No.2 and Alcaraz from matching Nadal and Djokovic as only the second rivals in tennis history to square off in four successive men's grand slam finals.
But the top-seeded Alcaraz's progression earlier was laced with drama and controversy.
Cruising two sets to love up, Alcaraz started cramping at 4-4 in the third set.
"It's f***ing bulls**t," a livid Zverev screamed at his box after raging at the tournament supervisor while Alcaraz received courtside treatment.
Under tennis rules, players are not allowed medical time-outs to treat cramping.
"This is not an injury. This is a cramp. They've totally botched this. That's why Zverev is melting," two-time Open champion Jim Courier said in TV commentary.
The tournament doctor disagreed, saying Alcaraz was injured, much to Zverev's dismay and anguish.
Runner-up last year to Sinner, tennis's nearly man Zverev had been striving to make his fourth grand slam final - and he certainly had his chances on Rod Laver Arena, before and after Alcaraz's body betrayed him.
The two combatants went blow for blow from the baseline in the opening set until Zverev double-faulted at 4-4 to gift Alcaraz the first break of the match.
The world No.1 duly closed out the set at the first time of asking to seize the early ascendancy.
Zverev served for the second set at 5-3 only to falter as Alcaraz, once again, raised his game when it mattered most.
The hobbling and hurting six-time grand slam champ battled on desperately trying to snatch the third set - and the match - in the tiebreaker.
Unable to, Alcaraz then relied on litres of pickle juice and multiple leg massages to help him recover sufficiently enough to compete.
His movement improved in the fourth set, but not enough to prevent Zverev from levelling the match in another tiebreaker.
Alcaraz had never lost a grand slam match from two sets up but was staring down the barrel at 3-5 in the fifth.
Yet again, though, he rallied back, reeling off four successive games to progress.