Having suffered heartbreak at Melbourne Park in back-to-back final defeats by Novak Djokovic and Rafa Nadal in 2021 and 2022, former US Open champion Medvedev will hope to get third time lucky when he meets Italian youngster Jannik Sinner on Sunday.
Russian Medvedev positioned himself well behind the baseline to counter Zverev's booming serves and extend the rallies but he fired a series of early double faults to fall behind. He clawed his way back from two breaks down to draw level at 5-5.
He admitted he was "a little bit lost" in the opening two sets.
"But during the third set I just kept saying to myself that if I lose this match I just want to be proud of myself," said the 27-year-old, who is into his sixth final at a major.
"I want to fight until the end, fight for every point. And I managed to win and I'm very proud."
Zverev struck again to move in front and raised his arms to huge applause after taking the first set with a superb backhand volley, having set up the opportunity by winning the previous point after an exhausting 51-shot rally.
He came into the net more and broke for a 3-2 lead in the second set which effectively helped him wrap it up, but Medvedev did not give up despite looking like he had just run a marathon and pinched the third set in a tiebreak.
Medvedev continued to push hard in a tense fourth set and he shrugged off a double fault in the tiebreak to level the contest, before breaking in the fifth game of the decider to lay the platform for his great escape.
