The world number four was forced to come from a double break down in the opening set against Bulgarian qualifier Tomova on Wednesday.
But Osaka, operating without the left knee brace she wore throughout the US Open, began to work through her repertoire and hit 40 winners, including 13 aces, to close out a 7-5 6-3 triumph.
"I know in the first set, I just started slow, and then in the second set, I just made a lot of really bad decisions in the first game," top seed Osaka told reporters afterwards.
"Other than that, I knew that I was the power player, and that I was the one that was kind of dictating how the match would go.
"It gave me a little bit of comfort knowing that if I just dialled down my unforced errors, I was going to win."
Osaka could face Yulia Putintseva in the quarter-finals, her Wimbledon conqueror who has won all three of the previous meetings between the pair.
First, though, Putintseva must get past Varvara Flink on Thursday.
Fellow seeds Angelique Kerber, Madison Keys and Elise Mertens all joined Osaka in the last eight.
Kerber claimed her first victory since Wimbledon by beating American qualifier Nicole Gibbs 6-2 6-4.
The three-time grand slam winner found herself a double break down in the second set but reeled off five consecutive games from 4-1 down to break a five-match losing streak.
"It's nice to have a win again," Kerber said. "The goal now is to finish the year as well as I can, to put all the energy which I have into this run in Asia and to play well in the next few weeks."
Keys is up next for Kerber after the American came from a set down to beat qualifier Zarina Diyas 5-7 6-0 6-4.
Belgium's Mertens was also forced into three sets by Hsieh Su-wei, eventually prevailing 6-3 1-6 6-2.