But Osaka impressed by winning the first set in 30 minutes before moving 3-1 ahead in the second.
She broke again for a 4-2 lead when Ostapenko netted a forehand and served for the match at 5-3.
But her 28-year-old opponent saved a match point on a forehand crosscourt winner and broke back when Osaka sent a forehand beyond the baseline.
Ostapenko, though, was broken again to love in the final game, with the Latvian netting a backhand to conclude matters after an hour and 12 minute.
“Granted, she broke me a couple times, but she’s a really good returner, so I can’t take that personally,” said Osaka.
“I went in there knowing she’s a great player and if I give her a chance she’s going to hit a winner on me, so I just tried to keep my pace and stay as solid as I could.”
Britain’s Emma Raducanu is also in action later, when she takes on American fifth seed Amanda Anisimova.