Williams, seeded seventh at this year's tournament, downed unseeded Maria Jose Martinez Sanchez of Spain, 6-1, 7-5.
"I was happy with that one," Williams said. "The first set was pretty clean (but) the second set she changed her strategy, started playing better and much more aggressively."
Serbia's Jelena Jankovic, the second seed, advanced to the fourth round with a 2-6, 6-4, 6-2 win over Caroline Wozniacki of Denmark, despite slipping and slightly injuring her left knee in the first set.
"I was disappointed with my performance throughout the whole match," Jankovic said.
Fifth-seeded Elena Dementieva of Russia was a 7-6 (7-2), 7-5 winner against Argentina's Gisela Dulko.
Also winning on Saturday were Thailand's Tamarine Tanasugarn, Shahar Peer of Israel, and Russians Nadia Petrova and Alla Kudryavtdseva.
The fourth round will be played on Monday following Sunday's normal open date at Wimbledon.
Celebrity Couples of 2014 [PHOTOS]