The 12th seed is a three-time finalist at Melbourne Park but never lifted the trophy, twice losing after taking a two-set lead including in 2024 when he was run down by Jannik Sinner.
Medvedev made no mistake in his opening round on Monday, downing young Dutchman Jesper de Jong 7-5 6-2 7-6 (7-2).
The 29-year-old former world No.1 looked in control in the third set, serving for the match at 5-4.
But world No.73 de Jong broke him twice to force the tiebreaker, which Medvedev was able to dominate, blasting a forehand winner from out wide on match point.
It was the Russian's sixth win in a row since arriving in Australia, taking out the Brisbane International, and bodes well after an uncharacteristically lean year, where he only won one match at all grand slams apart from Melbourne, where he reached round two.
"Today was not easy, first match different tournament - a grand slam - and last year I lost almost everywhere first round, except here," former US Open champion Medvedev said.
"I'm happy to win in straight sets even if some of them were kind of up and down.
"Conditions felt slow so we were both breaking each others' serves but the most important (thing) is to win and hopefully I can play better next round."
Meanwhile, injury forced seventh-seeded Canadian Felix Auger-Aliassime to retire early in the fourth set of first-round match against Nuno Borges.
The Portuguese player led 3-6 6-4 6-4 when Auger-Aliassime signalled he could not continue due to an upper left leg injury.
Auger-Aliassime called a medical time-out late in the third set and again received treatment before the start of the fourth set but after playing two points he retired.
The 25-year-old was looking to continue his impressive recent grand slam form, reaching the semi-finals of last year's US Open.
World No.46 Borges, who reached the last 16 in Melbourne in 2024 and the third round last year, said he felt for Auger-Aliassime but was pleased with his own performance.Â
"It's a great win for me either way. I thought I competed well. Maybe if he was 100 per cent, it would've been a different score, but I'm really happy to push through this one and get another opportunity," the 28-year-old said.
In other results, 13th-seeded Russian Andrey Rublev breezed past Italian Matteo Arnaldi 6-4 6-2 6-3, while world No.20 Tommy Paul also posted a comfortable 6-4 6-3 6-3 win over fellow American Aleksandar Kovacevic.
