But Osaka won the first set in 30 minutes before taking a 3-1 lead in the second game.
When Ostapenko got the forehand and played 5-3, she led 4-2 again.
But her 28-year-old opponent saved a match point in the forehand crossing and fell when Osaka sent a forehand that surpassed the baseline.
However, Ostapenko was broken again in the final match, with Latvian finishing backhand after an hour and 12 minutes.
Emma Raducanu of the UK is also taking action when accepting the fifth seed of the United States, Amanda Anisimova.
