(CNN) Serena Williams progressed to the semifinals of the Rogers Cup on Friday by defeating Naomi Osaka 6-3 6-4, the first time the pair had met since the infamous US Open final in September of last year.

Despite the loss, Osaka, who crashed out of Wimbledon in the first round last month, will return to the world No. 1 spot on Monday following Ashleigh Barty's opening round defeat in Toronto.

Williams, meanwhile, who was recently ousted by Simona Halep in the Wimbledon final , looked in fine form against her Japanese opponent as she surpassed Arantxa Sanchez Vicario's record of 32 Rogers Cup wins.

There was no repeat of the scenes that marred last year's Grand Slam final in New York when Williams was docked a game after clashing with umpire Carlos Ramos, calling him a "thief" and accusing him of double standards that favored male competitors.

Williams defeated Osaka in straight sets at the Rogers Cup.

The pair seemed evenly poised in the opening set until Williams broke in the seventh game. With a 5-3 advantage, she held serve to take the first set.

It was her fine serving form that proved to be Williams' greatest asset in Toronto, hitting 12 aces in total and winning 82% of points on her first serve.

She broke Osaka early in the second set and held out to claim the victory, sealing the contest with an ace after Osaka had saved three match points.

The American has yet to drop a set so far in the tournament and will now face Czech qualifier Marie Bouzkova in the final four in a bid to win her fourth Rogers Cup title.

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After the match, Osaka spoke of her admiration for Williams, whom she has beaten on their two previous meetings.

"This is someone that I looked up to forever," said the two-time Grand Slam champion.

"So in a weird way, losing today I accomplished my dream. I know that sounds kind of weird, but, you know, if there's anyone in the world that I would want to lose to -- of course I would never want to lose -- but I don't mind losing to her because I learned a lot.

"And this is someone that I kind of modeled my game after when I was little. So this is such a big learning experience for me."

The 21-year-old has previously dubbed Williams her "tennis mom." When asked about this in her post-match interview, Williams, who is 16 years Osaka's senior, quipped that she's "more or less her tennis grandma."

"It was a better match for me today," she continued. "We haven't played since New York, which was a really good match for her. I just wanted to come out and try and win a set this time because she's beaten me twice.

"I just wanted to do the best I could today."