A win for Williams sees her bounce-back after losing in disastrous conditions at the Arthur Ashe Stadium in NY, when the 37-year-old received code violations for coaching, smashing her racket, and calling the umpire Carlos Ramos a "thief" at the 2018 US Open.
Williams won in straight sets, 6-3, 6-4, to advance to the Rogers Cup semifinal in Toronto, and is one win away from the competition final, where the victor will receive 1,000 ranking points.
"I knew her game a little bit more, so that's a little easier", Williams said after the match, according to the Times. "All the emotions I had in the tiebreaker. and just with all that I've been through".
"I grew up watching her", said Osaka on Thursday.
Bouzkova started strongly before being overpowered 1-6 6-3 6-3 by 23-time Grand Slam champion Williams. Williams was penalized for illegal coaching, breaking her racket and verbal abuse, and later suggested that the umpire's actions were motivated by sexism.
There was no such drama in Toronto, where Williams broke Osaka for a 5-3 lead in the first and closed out the opening set with a service victor.
"It feels more like I'm showcasing my skills to her, like, 'Look what I can do.' You know what I mean? This debacle ruined something that should have been incredible and historic".
She broke Bouzkova in the next game to finally take control and end the Czech's breakout week.
"I honestly don't really think there was ups and downs", Osaka said. Japan's World Number one tennis player felt the same as she used to feel a few months ago when she won in Melbourne. "I think that the results, of course, will show, but I have to not think too much about winning or losing". "Just hopefully just being able to stay in the rhythm and playing this week and next week would be good".
"In the third set I told myself, 'Go big or go home, ' " Andreescu said.
One comfort for Osaka is that she will return to the top of the world rankings next week.
Serena Williams (USA) plays a shot against Marie Bouzkova (Czech) during the Rogers Cup tennis tournament at Aviva Centre.
Pliskova eliminated Estonia's Anett Kontaveit 6-3, 7-5 to set up a last-eight clash with rising Canadian star Bianca Andreescu, who outlasted fifth-seeded Dutchwoman Kiki Bertens 6-1, 6-7 (7/9), 6-4.