Four-time winner Williams, who needs to make the semi-finals to avoid dropping out of the top 100, eased past Russia's Maria Kirilenko 6-3, 6-2 in easily her most dominant display at the tournament so far to reach Monday's fourth round.
Williams will face France's Marion Bartoli, the 2007 runner-up, who made the last 16 after beating Italy's Flavia Pennetta in a tense affair where she kicked her own father off court.
Seventh seeded Williams had come into her 12th Wimbledon on the back of an 11-month injury lay-off, recovering from a foot injury and life-threatening blood clots on her lungs.
But after needing three sets to see off Aravane Rezai and Simona Halep in her first two matches, the 29-year-old looked back to her best on Court One.
She fired down 10 aces and 32 winners past the outclassed 27th-seeded Kirilenko, wrapping up victory on her third match point.
"I'm feeling better and glad to still be in the tournament," said Williams.
"I just need that rhythm that I have been missing and keep serving like I did did today."
Fifth seed Sharapova saw off Klara Zakopalova of the Czech Republic 6-2, 6-3 and will tackle China's Peng Shuai for a place in the quarter-finals.
"I haven't been past the fourth round for a few years so I am happy to get where I am. I hope to go one step further and even more," said Sharapova.
"It's great to be in the second week. The opponents will get tougher but raising your level is what it's all about at the grand slams."
Peng, the only Chinese player left in the draw after the second round exits of French Open winner Li Na and Zheng Jie, reached the fourth round for the first time with a 6-2, 7-6 (7-5) win over unseeded Hungarian Melinda Czink.
Top seed Caroline Wozniacki reached the fourth round for the third successive year with a 6-3, 6-2 win over Australia's Jarmila Gajdosova.
Wozniacki, still searching for a first grand slam title, will next face Slovakian 24th seed Dominika Cibulkova who booked her last 16 place with a 6-4, 1-6, 6-3 win against German 16th seed Julia Goerges.
"I'm really happy about the way I played. Jarmila has a great game for grass with a big serve and big forehand," said the 20-year-old top seed.
Bartoli was involved in an extraordinary on-court bust-up with her father who she banished from the stands on her way to beating Pennetta 5-7, 6-4, 9-7.
Bartoli ordered her father and coach Walter, as well as her mother, from the court after the first set.
"I was so tired and exhausted that really I had to express my emotions somehow," said the 26-year-old Frenchwoman.
"I saw them after the match and they understood completely. It was not against them. It was just that we played a very long first set, and I was exhausted and I was tired and I was feeling worse and worse."
Two former French Open champions made their exits from the tournament.
Ana Ivanovic, the Serb 18th seed and a former world No.1, crashed out 6-2, 7-6 (7-0) at the hands of Czech world No.81 Petra Cetkovska who had not won a match on tour all year before Wimbledon.
Francesca Schiavone, the 2010 French Open winner and Roland Garros runner-up just three weeks ago, lost 3-6, 6-4, 11-9 to Austrian world No.80 Tamira Paszek.
Meanwhile, big-hitting Sabine Lisicki, who knocked out French Open champion Li Na in the second round, made the last 16 for the second time in three years by defeating Japanese qualifier Misaki Doi 6-4, 6-2.
- AFPTags: sport, tennis, england First posted June 25, 2011 22:55:00