Williams, as the No. 2 seed, had a first-round bye but pulled out of the tournament before play began Wednesday. That gave Marion Bartoli a walkover into the quarterfinals.
Victoria Azarenka, whom Williams replaced last Monday as the No. 1-ranked player, said a foot injury forced her to leave the Dubai tournament.
That leaves defending champion Agnieszka Radwanska as the highest seed in the tournament. She defeated Yulia Putintseva 7-5, 6-3 in her second-round match by going 6-for-6 in break-point opportunities.
No. 8-seeded Caroline Wozniacki blitzed Zheng Jie 6-0, 6-1 in 54 minutes, losing only eight points in seven games serving. Nadia Petrova also had a lopsided win, beating Carla Suarez Navarro 6-1, 6-0 without facing a break point. Suarez Navarro had taken Azarenka's spot in the draw.
Thursday's quarterfinals have Errani going against Petrova and Stosur facing Vinci in the top of the draw while Radwanska plays Kvitova and Wozniacki meets Bartoli in the other matches.