Osaka, who won the Indian Wells Masters tournament in March, fired nine aces and produced 32 unforced errors, 10 fewer than her Belarussian opponent, in a gusty defensive performance.
Sabalenka, who saved three break points in the final set, flung her racket in dismay after committing a double-fault on match point, handing victory to her 19th-ranked opponent.
An emotional Osaka wiped tears from her eyes in an on-court interview, thanking the crowd and saying she would not have forgiven herself had she lost.
"I was just thinking I have to fight for every point; even if I break a leg I should try to get to every ball," she said.
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Osaka said Sabalenka's blistering serve had been a key challenge to overcome toward the end of the match.
"I felt like I had a lot of chances to break her in the third set, then she would serve these really amazing serves. Like a part of me knew it was coming, but at the same time I was always very unprepared," Osaka said. "I'm just real glad I was able to win in the end."
She next faces Lesia Tsurenko of Ukraine.
(Reporting by Amy Tennery; Editing by Ken Ferris and Pritha Sarkar)
