The best progression of the week came from the Greek Maria Sakkari who reached the semi-finals in Florida after knocking out Osaka. The 25-year-old Athenian moves up six places to 19th, her highest ranking yet.
Barty, the 2019 French Open champion, has held the No 1 ranking since September of that year, despite skipping the rescheduled US and French Opens in 2020 to remain in Australia.
Seventh-seeded Spaniard Roberto Bautista Agut beat Medvedev 6-4, 6-2, for his third win in as many meetings with the Russian.
Miami Open: Maria Sakkari ends Naomi Osaka's winning streak to reach semi-finals; Andreescu advances
Osaka broke in the second game of the second set and seized a 3-0 lead before Sakkari roared back to seal a semi-final spot in the prestigious ATP Masters and WTA hardcourt tournament.
Aryna Sabalenka, Elina Svitolina, Andrey Rublev, Diego schwartzman expressed uncertainty about taking the COVID-19 vaccine shot.
Miami Open: Naomi Osaka, Ashleigh Barty, Bianca Andreescu in quarter-finals; Stefanos Tsitsipas into last-16
The world's top-ranked player Ashleigh Barty has reached the Miami Open quarter-finals, getting there by holding off 14th-seeded Victoria Azarenka of Belarus 6-1, 1-6, 6-2
Medvedev failed to convert three match points in the second set after taking a 5-2 lead. An hour later the Russian was still playing, and on a humid afternoon with temperatures in the mid 80s, he paid a price.
Second-ranked Osaka, the reigning US and Australian Open champion, will next face the winner of a later match between 16th seed Elise Mertens and 22nd-seeded Anett Kontaveit.
Thirteen aces among her 36 winners helped Osaka overcome a slew of unforced errors of her own and set up a third-round meeting with Serbian qualifier Nina Stojanovic, who surprised Yulia Putintseva
Naomi Osaka withdraws from Stuttgart Open, to begin clay court season 'a little later,' say organisers
"Naomi Osaka will now begin the European clay court season a little later in May," said the Stuttgart organisers in a statement.
The 24-year-old from Queensland elected not to travel outside Australia after the WTA Tour resumed last year, skipping both the US Open and the rescheduled French Open at Roland Garros in September.
The elder Osaka was ranked 340th in the world, having reached a career-high of 280th in 2018, and last played a singles tournament in January.
WTA CEO Steve Simon said in a statement that the tour is "currently reviewing if any further adjustments to the rankings process will be made."
What was mind boggling was that Barty’s 1351 points lead over Naomi Osaka and 1931 points over Simona Halep was due almost entirely to tournaments she had played (and done well at) over a year before.
Naomi Osaka has four Grand Slam titles, and remains unbeaten in major finals after lifting the 2021 Australian Open. But more remarkably, each of her Slam has been significant to her as a player and a person.
Osaka, 23, trades places with Simona Halep, the Romanian dropping down to third after losing to Serena Williams in the quarter-finals.
Australian Open 2021 Review: Naomi Osaka and Novak Djokovic's contrasting roads to glory highlight year's opening Slam
In the end, the ‘new normal’ turned out to be the ‘old normal’ at the Australian Open 2021. Novak Djokovic and Naomi Osaka lived up to their billing of being the tournament favorites by capturing the men’s and women’s titles. However, the two are a study in contrast in almost everything and had very different journeys to their titles.
23-year-old Naomi Osaka won her fourth Slam from the last eight she's contested. She became only the third player after Monica Seles and Roger Federer to win their first four major finals
Osaka's triumph over Jennifer Brady in the Australian Open final was hailed in Japan, and beyond, as astronaut Soichi Noguchi wrote from space "Naomi Osaka, congratulations on the victory," with a gold-medal emoji.
Australian Open 2021: Jennifer Brady says winning a Slam no longer feels as improbable as 'going to Mars'
Brady reached the Melbourne final despite undergoing 14 days' hard quarantine in Australia, forced to stay in her room while other players were allowed out every day to train.