Serena Williams 'getting there' after avenging US Open defeat to Naomi Osaka at Rogers Cup

Serena Williams did not face a single break point during her victory over Naomi Osaka at the Rogers Cup. AFP

Serena Williams insisted there is more to come from her after earning a measure of revenge against Naomi Osaka in the Rogers Cup quarter-finals on Friday night.

Williams, who lost to Osaka in the US Open final last year in controversial fashion, claimed a 6-3, 6-4 win over the Japanese star, who still had reason to celebrate having reclaimed the No 1 ranking.

Williams fired 12 aces and didn't face a break point as she beat Osaka for the first time in three meetings - avenging her loss in last year's US Open final in which the American was docked a point and a game after losing her temper when warned about coaching.

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 winner. She broke again for a 2-1 lead in the second and never looked like surrendering the advantage.

Even a run-in with the net cord - as she raced forward trying to run down a drop shot -- didn't faze her.

"It hurt, but it wasn't the end of the world," Williams said.

The American's lone wobble came in the final game. After a pair of aces gave her a triple match point, Williams offered up a double fault and two backhands into the net before she closed it out with an ace on her fourth match point.

"We haven't played since New York, which was a really good match for her," said Williams, adding that she feels her own game is coming on as she'd hoped in the buildup to this year's US Open at Flushing Meadows.

"I'm getting there," said Williams, who hasn't dropped a set this week as she pursues a fourth Toronto title to go with those she won in 2001, 2011 and 2013. "It's definitely not where I want to be, but I'm getting there."

Osaka said she played too defensively - something she said was hard to avoid when Williams was hitting 31 winners.

"But I think there were chances where she hit shorter balls, but I wasn't expecting her to hit the shorter balls, so I didn't move up on time," she said.

In the semi-finals Williams will face Czech qualifier Marie Bouzkova, who advanced when Wimbledon champion Simona Halep retired with Achilles tendon trouble after dropping their first set 6-4.

"I've always wanted to play Serena," said Bouzkova, a 21-year-old ranked 91st in the world. "It's always my dream to play against her."

Bouzkova notched her third straight win over a grand slam champion, having beaten former US Open winner Sloane Stephens and former French Open champ Jelena Ostapenko.

The Romanian, who roared back from 0-4 down to level the set at 4-4 only to lose the last two games, said she had been bothered by her Achilles tendon from the start of the tournament.

"And today I felt it more, so that's why I decided to retire," said Halep, no doubt exercising extra caution with the final grand slam of the year due to start on August 26.

Despite the defeat, Osaka is assured of a return to world No 1 next week after the second-round exit of top-ranked Australian Ashleigh Barty and a quarter-final defeat for third-ranked Czech Karolina Pliskova.

Canadian teen Bianca Andreescu ousted Pliskova 6-0, 2-6, 6-4 after one hour and 49 minutes to doom the Czech's bid to regain the top spot for the first time since 2017.

Andreescu advanced to a semi-final clash with American Sofia Kenin, who defeated Ukraine sixth seed Elina Svitolina 7-6, 6-4.