"I definitely see myself in the top 10, but, right now, I'm not looking at that," Williams said. "I'm just trying to play every match to do the best I can."
Davenport, who reigned as the world No 1 for 17 weeks from last October, is suffering with a respiratory infection. The Evert Cup champion in 1997, Davenport is taking a second course of antibiotics to clear congestion in her lungs.
The match started with Davenport having two chances to break Williams' serve in the first game and one chance in the third game of the first set. Failing to take advantage, Davenport was never able to create another opportunity to challenge Williams. It was the second time in the three matches they have played each other that Williams has emerged victorious. "I thought probably it was more me than more her," Davenport said. "She definitely took advantage of a good day to beat a top player. I just never felt all that great about my game. I wasn't ready to play my best tennis when I had to."
By the second set, Davenport was having difficulty controlling her shots with numerous forehands flying well beyond the court boundaries.
Williams had 10 chances to break Davenport's serve in the 65-minute match and was successful on three occasions - the final game of the first set and the second and eighth games of the second set.
The fifth-seeded Steffi Graf faced little resistance, beating Kvetoslava Hrdlikova, of the Czech Republic, 6-1, 6-2. The former world No1 announced that she will compete in next month's Hamburg tournament for the first time for five years. Graf won the event five successive times from 1987.
n The American Jan-Michael Gambill defeated Australia's Lleyton Hewitt 7-6, 4-6, 6-4 on Sunday to win his first ATP Tour title, the Franklin Templeton Classic in Scottsdale, Arizona.Reuse content