By Caroline Cheese
BBC Sport at Wimbledon
Serena admitted being frustrated by the wind on centre court
Two-time former champion Serena Williams survived a testing first set before seeing off 2006 winner Amelie Mauresmo 7-6 (7-5) 6-1.
The American struggled in the blustery conditions and committed 19 unforced errors in the first set.
However, she stepped up the power to edge the tie-break and that all but ended Mauresmo's challenge.
Hampered by a thigh injury, Mauresmo avoided a second-set whitewash by breaking at 0-5 before she succumbed.
"It was so windy, I couldn't make my shots so I was a little frustrated," Williams told BBC Sport.
"It was definitely intense. I didn't play my best but I was glad I was able to pull through.
"I haven't been playing my best but I'm thinking positive and I have so much more I can do. I think in the second week I should do a lot better."
I'm not going to talk about the second set
The first set did not make pretty viewing for the subdued Centre Court crowd and there were four breaks of serve as both Williams and Mauresmo struggled to find their rhythm.
The set was settled by a tight tie-break and in the end, Williams' serving proved the difference, and the American wrapped up the breaker 7-5.
Mauresmo sealed her fate when she gifted Williams an early break in the second, and when she slid to 3-0 down, she called the trainer to attend to her left thigh injury.
The Frenchwoman took a solitary game before Williams broke her again to complete victory in just under an hour and a half.
"I was not 100% in my movement but overall I thought there were some good moments in the first set," said Mauresmo.
"But I really started to feel the injury in the tie-break and I'm not going to talk about the second set."
Mauresmo, who had hinted at retirement earlier in the year, deflected talk about her future by saying her schedule would remain the same for now, and that she planned to be back at Wimbledon in 2009.
Williams now faces fellow American Bethanie Mattek in the fourth round after Matteck knocked out last year's finalist Marion Bartoli 6-4 6-1.
"I've played her before and I remember she gave me a good match" commented Williams.
"She's a nice girl but I want to be able to win. I'm just taking it one match at a time but I do put pressure on myself to do well and to win."