The Russian world No.13 was untouchable with his service game in the 6-3 6-2 second-round win over the American.
Medvedev did not allow Tiafoe to get a look at a break point and was only taken to deuce once on his serve.
The 29-year-old 2021 US Open winner reached the final of the Brisbane tournament in his only previous appearance in 2019 and is looking good to give himself a crack at going one better this time.
"I am happy with the way I served, much happier than the first round," Medevdev said.
"I didn't face a break point and that puts a lot of pressure on your opponent. I got a couple of good games on his serve and it was enough today."
Medevdev broke world No.30 Tiafoe once in the opening set and twice in the second to look untroubled on his way to victory.
The main event is of course the Australian Open where Medvedev has been a finalist on three occasions.
After losing to Novak Djokovic in straight sets in the 2021 final, in 2022 Medvedev was on track to beat Rafael Nadal in the final after winning the opening two sets, before losing in five.
Then in the 2024 final in Melbourne he lost in another five-set marathon to Jannik Sinner, after also winning the opening two sets.
That year he set an Open era record by playing for 24 hours and 17 minutes for the entire tournament, and also established a new mark for most sets played in a singles major - an incredible 31 sets.
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