Medvedev completed an all-conquering week to fight back from losing the opening set to extinguish de Minaur 1-6, 6-4, 7-5.
But not before the young Russian endured the hometown favourite's captivating third-set comeback from 4-0 down to very almost pull the rug right out from under his feet.
But the stubborn Russian qualifier won the mental battle, eventually wearing the local favourite down to prevail 1-6 6-4 7-5 in two hours and 12 minutes.
The Australian summer of tennis has been one to remember for De Minaur, who now finds himself just one win away from claiming his first ATP tour title at the tender age of 18.
"I didn't want to just not leave it all out there, especially for everyone who stayed out there". It's been a thrill, and I just want it to keep on going.
"I felt like it was a pretty good level", Barty said.
But De Minaur proved too steady, winning 6-4 6-4 to become the youngest male semi-finalist at the event in almost 30 years.More news: On to the next game for ´proud´ Tottenham record-breaker Kane
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De Minaur twice broke Dzumhur in the first set, and refused to let up in the second with an early inroad before the frustrated 25-year-old called it quits.
On the same day that Bernard Tomic failed to qualify for the Australian Open and proceeded to boast about money, de Minaur is a breath of fresh air.
He doesn't have the serve, power or flair of Kyrgios, not by a long shot, but you get the feeling a match between the two of them, with the stakes raised, would be a hell of a sight. I really cherish the moment and am thankful for all the supporters that come out there.
As it stands, world No.167 de Minaur is the lowest-ranked Sydney finalist since No.223 Andrei Cherkasov in 1989.
By the match's half-hour mark, de Minaur had already broken Medvedev three times and converted his third set point, much to the delight of the packed crowd at Ken Rosewall Arena. Then serving for the match at 5-4, he was easily broken by de Minaur, who had the home crowd roaring. The young sensation fought back from 0-4 down on Saturday night in a heart-stopping deciding set and saved a match point under enormous pressure at Sydney Olympic Park.
A win in the harbour city would have been a momentous occasion to savour, a first piece of silverware to reward the 18-year-old's breakout fortnight.