By his standards, the three-time Open runner-up arrived at Melbourne Park at a relatively low ranking of No.12 in the world following just one victory at last year's four grand slams.
But the former world No.1 feels like he is slowly warming to the task of re-emerging as a major title threat after taking out the Brisbane International and now moving into the last-32 in Melbourne with a four-set victory over Quentin Halys.
He was later joined by last year's finalist German Alexander Zverev, with the third seed downing Frenchman Alexandre Muller 6-3 4-6 6-3 6-4 in a Wednesday night match on John Cain Arena.
American Frances Tiafoe then set up a third round clash with Australia's main hope Alex de Minaur, beating Argentine Francisco Comesana 6-4 6-3 4-6 6-2.
Zverev was a set and 0-3 down, having lost seven games in a row, but turned his performance around despite a foot injury that required a mid-match painkiller.
"The way he came out, he played amazing tennis," the 28-year-old said of Muller.
"I thought it was a very high level match ... I'm extremely happy with this match."
Medvedev was delighted to finally string some major wins together.
"It's the first time in a couple of years I'm in the third round of a grand slam, so I'm feeling good," Medevedev said after taking out the Frenchman 6-7 (9-11) 6-3 6-4 6-2.
"I will be honest, I played much better in Brisbane.
"I feel like I still can't get exactly used to the court here. I feel like I'm missing a little bit of power on my shots, but it's good because while you continue winning, usually during the tournament you find it step by step.
"So, today, I had a bit more than the first match. Hopefully the next one I can have a bit more, but I'm definitely playing better."
Runner-up at Melbourne Park to Novak Djokovic in 2021, Rafael Nadal in 2022 and Jannik Sinner in 2024, the former US Open champion is not ready to say he is back to the level needed to contend again this fortnight.
"Tough, tough," he mused.
"But before when I was top four and playing almost semis or final in every big event where I played, I was of course thinking already kind of, 'OK, I need to like be good in these later stages now'.
"That's not the case. I need to rebuild my confidence step by step, so I take a match at a time.
"If I manage to win a lot more matches here and I manage to win five more, it's going to be great.
"But I'm just trying to enjoy to play some good tennis and I'll try my best."
Earlier, fellow Russian seed Andrey Rublev also advanced with a dominant four-set win over Portuguese Jaime Faria.
The 15th seed showed his fiery personality on Margaret Court Arena, losing focus in the fourth set after smashing a ball into the net.
But he overcame his emotions to claim a 6-4 6-3 4-6 7-5 victory.
American world No.20 Tommy Paul moved into the last 32 with a second consecutive straight-sets victory.
Paul eliminated Argentina's Thiago Agustin Tirante 6-3 6-4 6-2 to remain on course for another promising run, similar to his charge to the 2023 semi-finals.Â
Kazakhstan's 10th seed Alexander Bublik booked a place with his 7-5 6-4 7-5 win over Hungarian Marton Fucsovics.
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