The win by Williams has bigger ramifications, however, as it assured that Williams will replace Victoria Azarenka atop the women's tennis rankings as of Monday. At 31, Williams will be the oldest woman to be ranked No. 1.
Monday will mark the sixth time Williams will be No. 1. She first reached the top of the rankings July 8, 2002, and most recently was No. 1 Oct. 10, 2010. She's been ranked first for a total of 123 weeks, which is sixth most all-time.
Kvitova, who'd never before taken a set from Williams, made Williams earn the win Friday, however. Kvitova built a 4-1 lead in the third set but Williams had a break of her own and two saves that allowed her to even the match at 4-4 and had another break to get to 6-5.
Earlier Azarenka, looking to defend her Qatar Open title, defeated sixth-seeded Sara Errani 6-2, 6-2. She dropped serve once in each set but also had three breaks in each set.
Sharapova will go against Williams Saturday after she opened the quarterfinals with a 6-2, 6-4 win over eighth-seeded Samantha Stosur. Sharapova lost her serve just once as she fired 12 aces while winning two-thirds of the points on serve.
Williams is 10-2 in her career versus Sharapova, having won their last 10 meetings. Sharapova beat Williams twice in 2004.