"I was determined to take the opportunity and go for it," said Williams after posting her first career victory over the Spaniard in five meetings. "I'm pretty excited, it's a great feeling."
The top seed and defending champion, Lindsay Davenport, the 1994 champion, Conchita Martinez of Spain, and seventh seed Barbara Schett also recorded straight-set victories.
Davenport beat Anke Huber of Germany 6-2, 6-2, Martinez defeated the unseeded American Corina Morariu 7-5, 6-2 and Schett went through when Natasha Zvereva, of Belarus, retired with a right ankle strain at 2-6, 4-2.
Williams was playing her first tournament since losing in the French Open two months ago. However, she combined a blistering back-court game with a powerful serve to beat the four-times Grand Slam winner.
Tim Henman blasted his way into the quarter-finals of the ATP Tour event in Cincinnati and said: "I can beat anybody." The British No 1 defeated Nicolas Kiefer of Germany 6-4, 6-1 to set up a last- eight match with Yevgeny Kafelnikov.
The Russian could replace Pete Sampras as world No 1 this week and Henman said: "He's playing as well as anyone right now. I think there are four guys, Sampras, Agassi, Rafter and Kafelnikov, who have proved they can be consistently in the top four, but there are no reasons why I can't beat them."
Henman had every reason to be delighted with his form after failing to win a match in his first two tournaments of this year's American hard court season.
Henman, instead of trying to serve and volley, worked his way to the net at every opportunity and took the opening set with a lob which Kiefer smashed into the net.
The British player then attacked Kiefer's serve throughout the second set and breaks in the fourth and sixth games were enough to bring him his second success in four attempts against the German.
"I was very satisfied with the way I played," added Henman. "I felt like he was a slight favourite coming into the match the way he's been playing recently. I haven't been playing so well.
"But after the way I played a couple of nights ago [against John van Lottum] my confidence is definitely returning and this win can only continue that."
Kafelnikov, the fourth seed, set up his meeting with Henman after defeating Chris Woodruff of the United States 6-4, 6-4.
Sampras celebrated his 28th birthday with a 7-5, 7-6 victory over Rainer Schuttler of Germany, extending his winning streak to 19 matches.
The defending champion, Pat Rafter, joined Sampras in the quarter-finals after beating the 15th seed, Nicolas Lapentti of Ecuador, 6-2, 6-3.