Osaka had a hard-fought three-set win over Sara Sorribes Tormo in the previous round but had a smoother match against Sasnovich, who she had brushed past 6-0 6-0 on route to her U.S. Open triumph last year.
The Belarusian showed a little more resistance this time and Osaka was forced to save two break points on her way to taking the first set and comfortably saw out the second to set up a meeting with unseeded Belinda Bencic of Switzerland.
"I think I played well today. But I knew that I had to because I've played her twice before already and it was on hard court and then I didn't know what to expect today so I tried to stay as focused as I could," Osaka told reporters.
"I'm in a really good place right now. I feel like I'm having fun playing tennis again which is always a good thing and I always play well if I have that mentality."
Kvitova, Madrid champion in 2018, beat France's Caroline Garcia 6-3 6-3 to set up a re-match of last year's final with Kiki Bertens in the quarter-final.
Halep, champion in 2016 and 2017, will meet Ashleigh Barty of Australia after thrashing Viktoria Kuzmova 6-0 6-0, losing only 12 points in the entire match which she described as her best-ever performance.
"I think it was the best match that I have ever had. I remember once I won 6-0 6-0 in 2016 in Bucharest, the final but it's the best match and I'm happy with the way I played," the Romanian said.
Sloane Stephens beat Zheng Saisai of China 3-6 6-3 6-2 and will meet Petra Martic, who earned a second walkover in a row when her compatriot Donna Vekic retired in the third set of their match. Martic was leading 3-0 in the third, after losing the first set 4-6 and winning the second 6-3.
(Reporting by Richard Martin; Editing by Toby Davis)
