The News Agency of Nigeria (NAN) reports that the 34-year-old American won 6-2 6-3 to pass Roger Federer in the all-time list of matches won at the tennis majors.
Her sister Venus however went out in dramatic fashion, losing 4-6 6-4 7-6 (7-3) to Czech 10th seed Karolina Pliskova.
In the men’s draw, both Swiss third seed Stan Wawrinka and Argentina’s Juan Martin del Potro progressed.
Former French and Australian Open champion Wawrinka saw off Ukraine’s Illya Marchenko 6-4 6-1 6-7 (5-7) 6-3 to set up a quarter-final clash against 2009 champion Del Potro.
Del Potro had led Dominic Thiem 6-3 3-2 when the Austrian retired with a knee injury.
Wawrinka, who smashed a racquet after failing to serve out his match in the third set, will get the chance to make up for defeat by Del Potro at Wimbledon.
Pliskova, 24, was broken when serving for the match at 40-0 but recovered to convert a fifth match point and reach her first Grand Slam quarter-final.
Romanian fifth seed Simona Halep beat Spain’s Carla Suarez Navarro 6-2 7-5 to set up a meeting with top seed Serena Williams.
In the men’s doubles, Jamie Murray and Brazil’s Bruno Soares beat Brian Baker and Marcus Daniell 6-3 7-6 (9-7) to reach the last eight.(NAN)