Medvedev extends strong start to season ahead of Australian Open
The Brisbane top seed took just an hour to defeat the American 6-3, 6-2 following his equally ruthless first-round win over Hungary's Marton Fucsovics on Monday.
Medvedev served superbly against Tiafoe and didn't face a break point in reaching the third round.
The 29-year-old Russian has conceded that the world's top two, Carlos Alcaraz and Jannik Sinner, are out of reach of the other players on the men's tour.
But he also said that anything could happen at a Grand Slam and he has shown in the first two rounds in Brisbane that he will be one of the challengers when the Australian Open starts on January 18.
"I'm really happy with the way I played the two matches," said Medvedev, a three-time beaten finalist at the Melbourne major.
"It's kind of continuing what I started doing at the end of the last year, already playing better and better.
"But these two matches (this week) I think were even better and I'm happy that some things I worked in the pre-season seemed to work here."
Defending champion Jiri Lehecka's was forced to retire from his match against Sebastian Korda of the United States.
Korda won the first set and they were on serve in the second when Lehecka pulled out with an ankle injury.