The World No. 1 outlasted the German third seed 6-4, 7-6 (7/5), 6-7 (3/7), 6-7 (4/7), 7-5 over a titanic five hours and 27 minutes in hot conditions.
He will play either Jannik Sinner or Novak Djokovic in Sunday’s title match.
But Alcaraz only narrowly avoided crashing out after a huge fright at 4-4 in the third set when he pulled up in pain with what appeared to be cramps.
He was allowed to have treatment at the changeover, leaving Zverev furious and angrily remonstrating with officials as medical timeouts are not permitted solely for muscle cramping.
The Spaniard continued but his movement was hampered and he lost his first set of the tournament before the pickle juice kicked in and he fought on.
Despite not being at 100 percent he somehow found a way to claw back from a break down in the fifth set as the crowd roared him on to leave the German shattered.
“Believing all the time,” Alcaraz, who is into his eighth major final and fourth in a row, said of how he got through.
“I always say that you have to believe in yourself no matter what, no matter what struggles you’ve been through, you’ve gotta still believe in yourself all the time.
“I was struggling in the middle of the third set. Basically it was one of the most demanding matches that I have ever played in my in my short career.”
Alcaraz has won two French Opens, two US Opens and twice at Wimbledon, but success on the blue Melbourne Park hardcourts has eluded the 22-year-old in four previous campaigns.
Should he snap the drought he would be the youngest man in the Open era to win all four majors, surpassing compatriot and legend Rafael Nadal, who was 24 when he did so.
The first set went on serve with few meaningful rallies until Alcaraz unleashed a backhand winner at 3-3 to earn the first break point of the match.
Zverev held on but the Spaniard worked another break point on his next serve with the German double-faulting as the pressure mounted.
Alcaraz served out for the set but the towering German kept his cool and raised his level to earn his first break points of the match at 3-2 in the second set.
The top seed saved two but whipped a forehand long to slide 4-2 behind.
Alcaraz sensationally broke back as Zverev served at 5-3 and it went to a tense tiebreak where the World No. 1 prevailed with a scorching forehand.
But disaster struck at 4-4 in the third when Alcaraz began limping badly.
He managed to hold for 5-4 but took a medical timeout, leaving Zverev fuming, before continuing to another tiebreak where the German made his move.
Despite the problems, Alcaraz continued winning points and holding serve in set four as his movement improved and another tiebreak beckoned with the third seed again coming out on top.
Zverev broke early in the fifth to move 2-0 ahead, but he folded when serving for the match with the top seed breaking back for 5-5 and then again to seal the win. (AFP)
