Osaka defeated Greece's Maria Sakkari 6-2, 6-7 (4), 6-3 on Tuesday to set up a second-round match with American Sofia Kenin.
The two-time Grand Slam champion and former world No. 1 took more than two hours and had 16 aces to beat Sakkari.
In other matches Tuesday, eighth-seeded Madison Keys beat Czech qualifier Maria Bouzkova 6-2, 6-3. Keys will now face local favorite Samantha Stosur in the second round.
"Sam's always tough," Keys said. "I think she's beaten me every time we have played. It's also hard to play someone who is going to be playing at home and have the crowd and all that."
Russian qualifier Liudmila Samsonova had the upset of the tournament so far by defeating American Sloane Stephens, the 2017 U.S. Open champion, 6-4, 2-6, 6-3.
Samsonova will face the winner of Tuesday night's match between two-time Wimbledon champion Petra Kvitova and Russia's Anastasia Pavlyuchenkova.
Wild-card entry Maria Sharapova was also set to play her opening match against American qualifier Jennifer Brady.