Barty, the first Australian woman into the final of her home Grand Slam since 1980, is looking to add to her 2019 French Open and 2021 Wimbledon titles.
Russia's Medvedev rolled through 6-4, 6-4, 6-2 in 1hr 55min, while Greek fourth seed Tsitsipas gained a 6-3, 7-5, 6-7 (2/7), 6-4 win over unseeded Frenchman Benoit Paire.
Defending Japanese champion Naomi Osaka has beaten Colombian rival Camila Osorio with 6-3, 6-3 and reached the second round of the Australian Open.
With the men's world number one Novak Djokovic flying home after being denied entry to defend his title, the tournament remains wide open with Rafael Nadal, Alexander Zverev, Daniil Medvedev and Stefanos Tsitsipas all in contention.
Serbian President Aleksandar Vucic has said authorities in Australia "humiliated themselves" and Prime Minister Ana Brnabic called the decision to deport tennis player Novak Djokovic "scandalous."
The tennis star's visa was cancelled over community health risk concerns, with the tournament set to begin on Monday.
World number one has been drawn for his first-round match while Australia's immigration minister still considers whether to deport Djokovic over his Covid-19 vaccine exemption.
None of the six contenders reached the required 75 percent of the vote in combined results from an official voting group and bonus percentage points awarded based on a fan vote.
World number one Novak Djokovic had scored a stunning courtroom victory on Monday, overturning the Australian government's decision to cancel his visa on Covid-19 vaccination grounds.
Novak Djokovic's lawyers have filed court papers in his challenge against deportation from Australia that show the tennis star tested positive for Covid-19 last month and recovered.
The 20-time Grand Slam singles winner will spend at least another night in immigration detention as he fights against the deportation move.
The decision to exempt World number one Novak Djokovic from Covid vaccination has provoked varied reactions ahead of this month's Australian Open.
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