Top-ranked Victoria Azarenka stayed on course to retain her Qatar Open title after dispatching Sara Errani 6-2, 6-2 Friday to reach the semifinals.
Maria Sharapova advanced by defeating 2011 U.S. Open champion Sam Stosur 6-2, 6-4.
Azarenka won all 14 net points in the match to make it 12 straight victories this year, including winning her second straight Australian Open title.
"The score never tells the whole story, really. We had a lot of really long rallies. I was expecting that. She's a very good fighter," Azarenka said. "I really felt like I took big advantage of the important moments, stayed aggressive, and really dictated my game."
The third-ranked Sharapova, looking for her third title in Qatar, will play either Williams, who beat Petra Kvitova to take the No. 1 ranking.
Sharapova broke twice to lead 4-1 in the first set. She took a 3-0 lead in the second before Stosur staged a brief comeback, but she missed a chance to tie it 4-4. The Russian closed it out when her backhand clipped the net and dropped over.
"I really started playing well when I had to and being aggressive at the right times," Sharapova said. "On the important points when I had to, I came up with really great first serves. That helped me win."