Zverev landed 94 of 111 first serves throughout the three hour, five minute contest and even when Alcaraz threatened a remarkable comeback he showed great composure to seal victory.
In his seventh Grand Slam semi-final, Zverev will need similar accuracy as he takes on Russia's Daniil Medvedev.
Alcaraz was outplayed for almost three sets but belatedly found his A-game to win a third-set tiebreaker with a mind-boggling flurry of outrageous winners.
Sixth seed Zverev was suffering from blood blisters on his feet during a riveting fourth set but held firm though to withstand the Alcaraz attack. His metronomic serving and bullet-proof backhand got him over the winning line against a top-five opponent for the first time at a Grand Slam.
"When you're up 6-1, 6-3, 5-2 against a player like Carlos you start thinking because we are all human," Zverev said on court.
"Your brain starts going and it's not always helpful but I'm happy I got there in the end. I fought back pretty well in the fourth set and didn't let go."
Zverev had spent nearly 14 hours on court to reach the quarter-finals while 20-year-old Alcaraz had roared through the draw and was firm favourite for Wednesday's clash.
But the Spaniard was caught cold as Zverev came out swinging, dropping only two points on serve as he raced through the opening set with ease.
Zverev failed to land only four first serves in the opening two sets and two breaks of the Alcaraz delivery in the second set enabled him to seize complete control.
A subdued Alcaraz looked at a loss to know what to do but when Zverev served for the match at 5-3 something clicked and he broke serve for the first time to stay alive - a huge smile spreading across his face as he sat down at the change of ends.
Suddenly playing freely, Alcaraz produced four successive winners from 0-2 down in the tiebreak as he reeled off seven points to take the match past midnight.
Whipping the late-night Rod Laver Arena crowd into a frenzy, Alcaraz looked favourite to take the match into a decider as Zverev began to hobble at times, but Zverev showed great resilience to hold serve in a pulsating eighth game which Nick Kyrgios, co-commentating for Eurosport, described as "insanity".
Some stunning backhands then gave Zverev the break of serve at 4-4 and 50 minutes after first serving for the match he managed to complete a remarkable victory.
