Osaka enjoys winning Madrid start in bid to end clay court jinx
The 23-year-old world number two recovered from an early break to ease into the last 32 in 87 minutes on the back of six aces, the last of which came on match point, and five breaks of serve.
For left-handed Doi, the world 79, it was a 21st loss in 21 meetings against top 10 players.
Osaka, the reigning US and Australian Open champion, has seven career hard court titles to her name, but has never managed to lift a clay court trophy.
The closest she came to breaking that run was a semi-final spot in Stuttgart in 2019.
"I try to play my natural way. I would say if I start thinking about grinding too much, I become a bit of a pusher and it's not really good for me," said Osaka who is playing her first clay court event since a third-round loss at Roland Garros in 2019.
"When I was playing on clay that year, I didn't feel uncomfortable at all. I didn't feel uncomfortable sliding or I didn't feel that tired.
"I definitely do feel a lot of extra pressure," said Osaka on facing other Japanese players.
"I never really know what to expect because I feel like she always plays better when I play against her, so it's a bit tough to manage controlling my emotions."
Sakkari dropped the opening seven games against Amanda Anisimova of the United States before hitting back to win 0-6, 6-1, 6-4.
Like Osaka, big-hitting Aryna Sabalenka of Belarus, a nine-time champion on the WTA Tour, is still seeking a first clay court title.
On Friday, the 22-year-old at least broke her Madrid duck after first round exits in 2018 and 2019.
Sabalenka was too strong for 36-year-old Vera Zvonareva of Russia, winning 6-1, 6-2 on the back of 37 winners.
Jessica Pegula of the United States defeated Romania's Sorana Cirstea 7-6 (7/5), 6-3.
Cirstea, 31, had won the Istanbul clay court title last weekend, her second career triumph coming 13 years after her first.
Romanian third seed Simona Halep, the Madrid champion in 2016 and 2017, defeated Spain's 46th-ranked Sara Sorribes Tormo 6-0, 7-5.
Russia's Darya Kasatkina, meanwhile, needed eight match points to knock out Romanian qualifier Irina-Camelia Begu 4-6, 6-4, 7-6 (7/1) in just over three hours.