World number one Naomi Osaka and world number three Simona Halep both won in straight sets to reach the Madrid Open quarter-finals.

Osaka beat Belarusian Aliaksandra Sasnovich 6-2 6-3 to reach the last eight in Madrid for the first time.

Halep took just 45 minutes to see off Slovakia's Viktoria Kuzmova 6-0 6-0.

The Romanian, who beat British number one Johanna Konta in the second round, is hoping to win the title for a third time after victories in 2016 and 2017.

Halep will play Yulia Putintseva of Kazakhstan or Australian Ashleigh Barty in the quarter-finals while Osaka will face Ukrainian Kateryna Kozlova or Switzerland's Belinda Bencic.

"I don't think it was her [Kuzmova's] best match. Maybe she was nervous before the match a little bit," said Halep,

"It's a big tournament and it's not easy to face the top players. I've been in that position. I played my best tennis and I felt good on court."