The 20-year-old, cheered by the capacity home crowd, raced into a 4-0 lead in the opening set and then went on break her opponent three times in the second to ease to victory.
"It was really difficult," third-seeded Osaka said courtside. "I'm just grateful that I could play in front of you guys."
Osaka will either play Barbora Strycova of the Czech Republic or Estonia's Anett Kontaveit in the quarter-finals.
Earlier in the day, two-time Grand Slam champion Garbine Muguruza suffered a shock 6-1 6-2 defeat by American qualifier Alison Riske.
World number 75 Riske scored her third victory over a top-20 ranked opponent this year, recording 19 winners to just nine unforced errors.
In her fifth quarter-final of the season, Riske will next face fourth seed Czech Karolina Pliskova.
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)
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