Azarenka, a mom who is eight years older than Osaka, was up a break in the second set, then failed to convert a break point to serve for the match before Osaka battled back.
Former No.1 Azarenka broke in the seventh game after saving a match point but Osaka wrapped up matters on her next service game on third match point after 2 hours 50 minutes.
Osaka found her rhythm and controlled the third set, firing three aces and 14 winners, while Azarenka trailed with seven winners and 15 unforced errors on the Suzanne-Lenglen court.
Osaka, 21, rallied from 4-0 down but was unable to salvage the opening set which Azarenka ended with a service victor. "I acknowledge that's kind of a toxic trait, but, like, it's gotten me this far, so..." After saving two break points, Azarenka doubled-faulted.
Her recent three-set routes to victory say less of a mortal tendency to drop sets when nervous and distracted, especially as a new face at No. 1, and speak more to her brilliance in outlasting tough moments: when strategy changes are needed, when margins are thin, when points are important.
After an 85-minute set, Azarenka stretched a bathroom break to 10 minutes before squandering three break points in the first game of the decider.
Azarenka mounted her own comeback, winning the next two games, but Osaka was able to capitalise on her second match point to seal victory.
"I have this mindset that I feel like I can win if it gets down to the wire, if I have to break a person".
Osaka will hope to avoid finding herself in more bother against Czech Katerina Siniakova as she tries to reach the fourth round here for the first time.
"She's been in those situations where those margins are really small", said Azarenka.
Asked about it after the win over Nara, she said: "I'm not going to get into that".
Williams will play Sofia Kenin, an American ranked No. 35, in the third round.
Tsurenko has never beaten defending champion Halep in seven career meetings, including two matches in February, but she said she was looking forward to the pair's third-round meeting. On his next opponent Salvatore Caruso, Djokovic said: "I never trained with him either".
The clay courts of Roland Garros host the second Grand Slam of the season.
World No. 91 Bublik delighted the Court Philippe Chatrier crowd with his wide range of shots, including three underarm serves in the opening set. Two younger contenders are in action: No. 4 Dominic Thiem, last year's runner-up, faces Pablo Cuevas, while No. 5 Alexander Zverev, a quarterfinalist in 2018, meets No. 30 Dusan Lajovic.
Edmund called on the trainer while trailing 7-6 (7/3), 6-3, 2-1 and, after a short discussion, he informed the umpire that he was unable to continue.
- India's Modi to hold bilateral meetings with visiting leaders after swearing
- Robert Pattinson is officially the next Batman
- Tensions High As Missouri Awaits Decision On Missouri's Sole Abortion Clinic
- Galaxy Note 10 Won’t Have Physical Buttons
- Draymond Green: 'It Wasn't Really a Scuffle' With Drake
- Hazard says "it'd be great" to face Chelsea next year — Real Madrid
- Trivia Tuesday: (Golden State) Warriors, come out to play
- Intel Unveils Its 10th-gen Processors at Computex 2019
- Chelsea prevail over Arsenal to take Europa League crown
- Mueller to Make First Public Statement About Russia Probe