Home fancy Alex de Minaur marched through in a 6-3 6-4 7-5 win over Frances Tiafoe on Friday night, but Medvedev was made to work when he trailed Fabian Marozsan by two sets to love.
After winning only one grand slam match in 2025, former world No.1 Medvedev dug deep to pull out a 6-7 (5-7) 4-6 7-5 6-0 6-3 victory.
"It was getting close to an end," the Russian conceded after edging to within two games of losing to the lowly-ranked Hungarian.
"It was a very tough match, and last year I lost probably all my grand slam matches when I was 2-0 down.
"Fabian played unbelievable in the first two sets. He played great and I was like, 'Look, if I lose, I lose, but I'm just going to try and fight'.
"I was not calm. Just think about what I need to do.
"My shots were getting better and better, even the first two sets they were not so bad, and so I did manage to stay calm for sure in the fifth set."
Unbeaten in eight matches this year, Medvedev faces an Open rematch on Sunday against young gun Learner Tien.
The 25th-seeded Tien beat Portugal's Nuno Borges 7-6 (11-9) 6-4 6-2 to back up his breakout fourth-round appearance in Melbourne last year.
In 2025, the American outlasted Medvedev in a five-set, second-round match that went into the early hours of the morning.
"I'm super happy," the 20-year-old Tien said.
"I actually played my third round last year on this court too, so this court's very special to me and I love playing on this court.
"Really physical match, especially the first set. Super-long first set, it would have been tough for either guy to lose that.
"So that was really big for me to get that first, and thankfully I was able to carry that momentum through the rest of the match."
The top-ranked Alcaraz continued his relentless march through the draw with a 6-2 6-4 6-1 dispatch of 32nd seed Corentin Moutet.
Alcraraz at times toyed with the Frenchman, notching his third consecutive straight-sets win of the week in a tick over two hours.
But the super Spaniard knows he will need to raise his game further next against world No.20 and 2023 Open semi-finalist Tommy Paul, who enjoyed a saloon passage through to the last 16.
The American was leading Spaniard Alejandro Davidovich Fokina 6-1 6-1 when the 14th seed retired with a leg injury.
Alcaraz has lost to Paul twice before, but not since 2023.
"We have a great battles against each other," said the six-time grand slam champ.
"It's always really difficult to play against him, so he plays great tennis on hard court - aggressive, great touch.
"So it's going to be a really interesting one."
Third-seeded German Alexander Zverev will take on Francisco Cerundolo after beating Briton Cameron Norrie 7-5 4-6 6-3 6-1.
The Argentine 18th seed Cerundolo was too good for Andrey Rublev, winning 6-3 7-6 (7-4) 6-3.
De Minaur will next meet 10th seed Alexander Bublik, who beat Tomas Martin Etcheverry 7-6 (7-4) 7-6 (7-5) 6.4.
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