Last year's runner-up, Li Na, beat fellow Chinese player Zheng Jie 6-3, 6-1.
Chinese fifth seed Li Na crashed out, losing 6-3 6-2 to 18-year-old American Madison Keys.
CNN: Tennis stars Federer and Nadal honor 'a very loved man'
Williams won the Madrid title last week and next faces French Open champion Li Na of China.
Fifth seed Li Na, who won at Roland Garros in 2011, suffered a shock defeat against Jelena Jankovic.
The Russian was joined in the next round by three former champions: Li Na, Svetlana Kuznetsova and Francesca Schiavone.
Hingis goes on to face Colombia's Catalina Castano, who upset sixth seed Li Na of China 6-4 1-6 6-2.
Earlier Zheng's compatriot Li Na followed her into the quarterfinals after stunning fourth seed Caroline Wozniacki in straight sets.
Victoria Azarenka, who won Saturday's women's singles final over Li Na, was also there with her boyfriend rapper Redfoo.
Sharapova will play either second-seeded Li Na or qualifier Bethanie Mattek-Sands for the title in the indoor clay-court tournament Sunday.
Zheng's compatriot Li Na followed her into the quarterfinals on Monday after stunning fourth-seeded Dane Caroline Wozniacki in straight sets.
Earlier, unseeded Clijsters beat China's Li Na in straight sets to continue her incredible comeback to tennis after a two-year layoff.
The 2011 French Open champion Li Na also progressed, the Chinese eighth seed recorded a 7-5 6-2 win over Hungarian qualifier Melinda Czink.
The 20-year-old Slovakian, ranked 58th in the world, claimed her first career title with a 6-0 7-6 victory over Chinese fourth seed Li Na.
Meanwhile, in women's action, Maria Sharapova crashed out in the semifinals of the Birmingham grass-court event, beaten in straight sets by China's Li Na.
Li Na has had an Andy Murray season, almost identical - good at Oz, struggle then come back on the clay, and coaching change...
In another big upset, China's Li Na, who reached the last four in the Australian Open, exited to British qualifier Elena Baltacha 7-6 2-6 7-6.
Home hopes will be carried into the next round by Zheng Jie and Li Na, who play Dinara Safina and Kaia Kanepi of Estonia respectively.
She'll face 2011 finalist Li Na in the final Saturday night.
Fourth seed Agnieszka Radwanska eased past Irina-Camelia Begu, while there were also wins for German fifth seed Angelique Kerber and China's sixth seed Li Na .
Dulgheru had put out Zheng's compatriot and third seed Li Na in the semifinals and will travel to Roland Garros as a dangerous outsider in the draw.
Russian No. 2 Sharapova will play 20th-seeded compatriot Maria Kirilenko, while the remaining quarterfinal tie pits China's French Open champion Li Na against German No. 18 Angelique Kerber.
There was no such trouble for Serena Williams in the women's event, as the world No. 1 reached the semifinals after seeing off a spirited Li Na of China.
Meanwhile, on the WTA Tour, China's Li Na reached the quarterfinals of the Stuttgart tournament with a straight sets win in her first match of the clay court season.
The five-time Key Biscayne champion advanced to Thursday's semifinals and tied the women's record for career victories in the tournament by beating No. 5-seeded Li Na 6-3, 7-6 (5).
Among the past Grand Slam title winners hoping to join her in the third round with victories Thursday: defending French Open champion Sharapova, Victoria Azarenka, Li Na and Petra Kvitova.
China's Li Na, seeded fifth, was also making a return after spending six weeks on the sidelines with an ankle injury but she eased past Dutchwoman Kiki Bertens 6-3 6-1.
U.K. designers including Burberry's Christopher Bailey, Matthew Williamson, Giles Deacon and Richard Nicoll created dresses for the opening party, dressing the likes of Li Na (Deacon) and Ana Ivanovic (Williamson).
应用推荐