Osaka, a two-time US Open champion, had not reached the third round at Flushing Meadows since 2021 but looked very comfortable as she booked a meeting with 15th seed Daria Kasatkina or Kamilla Rakhimova.
"I was just really trying to focus and not give her any free points and just be positive," said Osaka, who donned a sparkling purple kit and walked in with her Labubu charm she nicknamed "Arthur Flash" in honour of late American tennis pioneer Arthur Ashe.
Osaka has shown glimpses of her old form this year, reaching the Montreal final, and after trading early breaks, she used her trademark powerful forehand to break Baptiste in the sixth game.
Baptiste handed the 23rd seed a head start with a double fault on break point in the opening game of the second set, and a faulty first serve helped Osaka to another break in the fifth.
The home fans were audibly disappointed as the unseeded American served another double fault on match point, and Osaka, who also beat Baptiste in the Miami third round this year, enjoyed a muted celebration.
"I was really stressed the entire time," said Osaka, who hit 13 winners and four aces. "I'm really excited to be moving better."