It wasn't long until Medvedev regained his advantage, breaking the next game and aceing his way to a 1-6, 6-4, 7-5 victory to take home the Sydney International trophy.
The majority of the crowd in Sydney was cheering for Australia's De Minaur, but after the match, Medvedev had this to say: "I think it (the crowd) works for everyone".
"I wanted to compete until the last point. I left it all out there on the court", he said.
Next to nothing has stopped de Minaur this year.
It would have made him the youngest player to win the Australian Open tune-up tournament in nearly two decades, since his mentor Lleyton Hewitt achieved the feat at the same age.
Eighteen-year-old de Minaur beat Frenchman Benoit Paire to reach the final.
Juan Martin del Potro will return to the top 10 for the first time since 2014
"After the match, I didn't fall down or anything, but I'm really happy".
However he failed to hold serve in the very next game, before Medvedev held his nerve to serve it out.
As it stands, world No.167 de Minaur is the lowest-ranked Sydney finalist since No.223 Andrei Cherkasov in 1989.
He will now face world no.20 Tomas Berdych in the first round.
The Russian then managed to take control of the match, racing ahead to a 4-0 lead, but 18-year-old De Minaur - the youngest player to make the Sydney Internationals since Lleyton Hewitt - fought back.
De Minaur looked well on his way to his maiden ATP title when he breezed through the first set 6-1, before Medvedev stormed back and the Aussie appeared to feel the effects of a gruelling two weeks.
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