Serena Williams (right) beat Naomi Osaka in Toronto. Photo: John E. Sokolowski/USA TODAY Sports

LONDON - Serena Williams overwhelmed Naomi Osaka in a highly-anticipated rematch of their US Open encounter with a 6-3, 6-4 victory on Friday to enter the semi-finals of the Rogers Cup in Toronto, Canada. 

The 23-time grand slam winner triumphed in 76 minutes without facing a single break point, and will next face Czech qualifier Marie Bouzkova after Simona Halep was forced to withdraw with a left lower-leg injury after losing the first set 6-4. 

Despite defeat, Japan's Osaka will reclaim the world number one spot on Monday after world number three Karolina Pliskova was defeated 6-0. 2-6, 6-4 by Canadian Bianca Andreescu, following Ashleigh Barty's early exit to American Sofia Kenin. 

The 19-year-old Andreescu will face Kenin in Saturday's final four after she conquered Ukraine's sixth seed Elina Svitolina 7-6 (7-2), 6-4 earlier. 

Meanwhile in men's Montreal event, top seed Rafael Nadal rallied from a set down to beat Italy's Fabio Fognini 2-6, 6-1, 6-2.

"It was an up-and-down match, but a positive match for me," Nadal said. "I have been playing better and better."

Alexander Zverev and Dominic Thiem were eliminated by Russians Karen Khachanov and Daniil Medvedev in their respective quarter-final contests. 

Williams and Osaka had not met since their dramatic US Open final last year, where Williams was involved in a row with umpire Carlos Ramos after he docked a point for on-court coaching and then lost a full game as she showcased unsporting behaviour in her protests at the decision. 

The 36-year-old went on to lose the championship to Osaka, who claimed her first grand slam title with a 6-2, 6-4 win, but in Toronto, Williams dominated. 

Williams broke Osaka's serve in the eighth game of the first set to take the lead and limited Osaka to just 20 points as she claimed her first victory over the 21-year-old with her 12th ace. 

"I knew her game a little bit more, so that's a little easier. I'm just overall a little bit better," Williams said in an on-court interview.

"I know her game. I watch her a lot. I know what I needed to do to hopefully try to get a win today, and it helped a little bit." 

Defeat was bittersweet for Osaka because following the dismissals of Barty and third seed Pliskova, she ascends to the top of the women's rankings again. 

"I feel like that's a position that I think requires a lot of work," said Osaka.

"I just have to keep working hard and putting in effort, and I have to not think too much about winning or losing."

Four-time champion Nadal was broken twice by Fognini to fall behind after the first set but the Italian world number 11 could not capitalise. 

Fognini double-faulted in the second set to trail 2-0 as Nadal surged through to level the match. 

The world number two Spaniard then won 12 of the last 15 games to win in under two hours and enter the last four in the Rogers Cup for the first time since 2013. 

He will play either compatriot Roberto Bautista-Agut or Frenchman Gael Monfils, who will resume their quarter-final on Saturday after it was suspended by rain. 

Germany's Zverev, seeded third, made eight double-faults in an error-strewn display as he was beaten 6-3, 6-3 by Russia's Karen Khachanov. 

The second-seeded Austrian Dominic Thiem was stunned in 56 minutes with a 6-3, 6-1 defeat at the hands of Khachanov's compatriot Daniil Medvedev.

Medvedev and Khachanov will create Masters tournament history by competing in the first all-Russian semi-final at that level.  

The 22-year-old Zverev was erratic in his performance and after double-faulting for a fifth time, he snapped his racket before dropping the first set with a second break. 

"Sascha (Zverev) didn't play his best today," said Khachanov. 

"I know what he's capable of but on the other side, I would like to take credit for myself."

Another double-fault from Zverev handed Khachanov a match-winning break for 4-2 in the second set. 

The world number eight Khachanov faced two break points serving for the match at 5-3, but held on to prevail in 74 minutes. 

dpa