World number one Karolina Pliskova advanced to the quarter-finals of the WTA Toronto hardcourt tournament while a pair of high seeds Venus Williams and Angelique Kerber crashed out in straight sets Thursday.

Pliskova's opponent Naomi Osaka abandoned due to a muscle injury, leaving Pliskova to advance 6-2, 6-7 (4/7), 1-0.

After taking the first set, Czech top seed Pliskova was given a scare after Osaka fought back to level in the second set tie-break. But with Osaka clearly in discomfort, the Japanese teenager scratched in the decider.

It was a frustrating end for Osaka, who had to pull out of events in Prague and Madrid earlier this year with the same abdominal injury.

Elina Svitolina easily dispatched the 37-year-old Williams 6-2, 6-1 while American Sloane Stephens crushed two-time major championship winner Angelique Kerber by identical 6-2, 6-2 scores.

Pliskova meanwhile was left satisfied after pounding down 12 aces and not dropping her serve once.

She admitted however that she faces a tough challenge holding on to her world number one ranking.

"It's going to be tough," Pliskova said. "There are a few tournaments to go before the end of the year and I know Simona's (Simona Halep) behind me. I'll do my best to stay there as long as I can -- hopefully a few more weeks."

Pliskova will now face former world number one Caroline Wozniacki in the last eight.

Denmark's Wozniacki advanced to the last eight with a 6-3, 6-1 win over 10th-seeded Agnieszka Radwanska, a close friend.

Williams, who was the oldest player in the draw, fell behind 5-0 in the first set and failed to muster any sort of challenge against fifth seeded Svitolina.

"I was just trying to focus on my game and play one point at a time," Svitolina said.

"I was trying to be there in the right moment, move quick, look for the ball and play as deep as I could to make her feel uncomfortable.

"I needed to stay calm tonight and just really be focused on each point. I'm very happy that I could win in straight sets."

- Goes out with a whimper -

The seven-time Grand Slam winner Williams made 21 unforced errors to just 10 for Svitolina. Williams, who was involved in a fatal car smash two months ago, hit six winners in the one hour match.

Stephens needed just 58 minutes to send German third seed Kerber packing.

Stephens stepped up her game against Kerber after a couple of long three set wins against Yulia Putintseva and Petra Kvitova in the first two rounds.

"I'm just pleased to be playing well and just happy to be back on the court again," said Stephens. "In the first match, I played well, someone that I don't think I have ever played before. And then second match playing Kvitova she's a lefty, which I haven't played in a really long time. 

"The same thing today, I just really went out and played my game."

In other action on Thursday, France's Caroline Garcia defeated Catherine Bellis of the United States 6-4, 6-2. 

Garcia will face second seed Halep in the quarter-finals. 

Halep, the defending champion, bundled out Barbora Strycova of the Czech Republic in under an hour, winning 6-1, 6-0.

Elsewhere, Lucie Safarova of the Czech Republic defeated Ekaterina Makarova of Russia 6-3, 6-7 (3/7), 6-2.