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The 2019 Australian Open champion outlasted the gallant Briton, who is ranked 371 after a lengthy stint on the sidelines with a back injury, 3-6, 6-3, 6-1 in one hour and 47 minutes.
She next meets world number 14 Johanna Konta or Irina-Camelia Begu from Romania as she ramps up preparations for the Australian Open.
"After I lost the first set, I just wanted to fight as hard as I could and give my best effort," Osaka said. "I like long matches because I can judge the court and it helps with my fitness."
Boulter, appearing physically strong and unleashing ferocious groundstrokes, has impressed in Melbourne and knocked out teenage sensation Coco Gauff with a comeback three-set victory.
She matched Osaka's aggressiveness from the baseline in an absorbing first set, where she ran her error-strewn opponent ragged and was rewarded with two breaks to claim the first set in 39 minutes.
Osaka then lifted her intensity, opening to a 4-0 lead before Boulter unexpectedly peeled off three straight games. But the Japanese star refocused to force a deciding set, which she ran away with.
The three-time Grand Slam champion had comfortably beaten France's Alize Cornet in straight sets in her first competitive match since lifting her second US Open title in September.
Serena Williams, world number two Simona Halep and defending Australian Open champion Sofia Kenin are also in action on Wednesday.