Second seed Medvedev eventually won 6-7 3-6 7-6 7-5 6-4, becoming the first player to fight back from two sets down in Melbourne this year.
Fourth seed Tsitsipas earned a dominant straight-set win over Jannik Sinner.
The 23-year-old, beaten by Medvedev in last year’s semis, won 6-3 6-4 6-2.
Tsitsipas now has the opportunity to avenge that defeat against the Russian and reach his first Australian Open final.
