Andre Agassi, the second seed, got past Younes El Aynaoui, 5-7, 6-4, 7-6 (7-4), 7-6 (7-4).
Williams has not failed to get past the third round at a major championship since the 1999 French Open. Later that year, she captured her first career Grand Slam crown at the U.S. Open.
In January, the 21-year-old won her fourth straight major at the Australian Open.
Agassi, who won the first of his eight majors here in 1992, is into the fourth round at the All England Club for the ninth time in his career. He next plays Australian Mark Philippoussis.
Philippoussis edged No. 35 Radek Stepanek of the Czech Republic, 4-6, 7-6 (9-7), 6-4, 7-6 (8-6).