The longer the rallies the more risky de Minaur became and he claimed the opening set after winning six games on the trot.
After initially taking the first set 6-1, De Minaur looked to be on course for a straight-set victory.
With that in mind, De Minaur is hard to tip against here and one expects the young Aussie to finish the job and end a great week on a great high.
Little known prior to his great run in Brisbane last week, the 18-year-old is fast pushing himself forward as Australia's hottest teenage talent.
"It's been a roller coaster, and I honestly wouldn't have it any other way", de Minaur said.More news: Lakers' Buss supports Walton after LaVar Ball comments
Down 4-1, the young Aussie appeared well out of the contest, but two double-faults handed de Minaur a break point and Medvedev surrendered serve when he sprayed a forehand long.
The passionate Blues fan showed plenty of heart.
De Minaur was leading Damir Dzumhur 6-2 3-0 on Wednesday when the world No.30 retired to become the teenager's fourth top-50 scalp in a stunning week.
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".
The 21-year-old victor needed two hours and 13 minutes to beat his 18-year-old opponent 1-6, 6-4, 7-5, reports Efe news agency.
In the last four he will face France's Benoit Paire, who knocked out defending champion Gilles Muller by the same scoreline.More news: Amazon.com (AMZN) Upgraded at BidaskClub
"I mean, to make it through the qualies, there were so many circumstances", Medvedev said afterwards.
"He was, like, 15. I'm still going to get out there on court and leave it all out there, give it my best". Because he beat me - it was only me serving and he beat me.
"You were wonderful, I wouldn't be able to do this without you. He is going to be good".
Compatriots Nick Kyrgios, Thanasi Kokkinakis and Dylan Alcott tweeted their appreciation of De Minaur's fight and he even wowed former World No. 1 Andy Murray, as well as Japan's Naomi Osaka.
"And he's becoming good now".
"It's about letting him play tennis now. It's nice to see some young guys coming up".More news: Legal & General Group Plc Grows Holdings in Callon Petroleum (CPE)
But the day belonged to de Minaur who said he was determined to keep rolling along.