Williams, a five-time Wimbledon champion, was down 3-1 in the first set Friday before taking control and ousting the 26th-seeded Russian.
Kleybanova put up a good fight in the set, which turned into a slugfest from the back of the court.
Story continues below ↓advertisement | your ad hereWilliams will play the winner of the match between Australia's Jarmila Groth and German Angelique Kerber for a berth in the quarterfinals.
Clijsters, Henin set up showdown
Justine Henin and Kim Clijsters, two Belgians making Wimbledon comebacks, won to set up a fourth-round showdown Monday.
Clijsters, seeded eighth, beat No. 27 Maria Kirilenko 6-3, 6-3. Henin, seeded 17th, defeated No. 12 Nadia Petrova 6-1, 6-4.
No. 4 Jelena Jankovic beat No. 28 Alona Bondarenko 6-0, 6-3. No. 11 Marion Bartoli, the 2007 runner-up, defeated Greta Arn 6-3, 6-4.
Wimbledon Show Court SchedulesBenfica deny Di Maria reports
