Williams, a five-time champion at the grass-court major at the All England Club, needed just 49 minutes to dispatch South African Chanelle Scheepers 6-1 6-1, totalling 26 winners and committing just seven unforced errors in a near-faultless performance.
The top seed will now face France's Alize Cornet in the third round following her 6-4 5-7 6-3 win over Petra Cetkovska of the Czech Republic.
Meanwhile, Sharapova looks well set to repeat her 2004 success, the Russian dismantling Switzerland's Timea Bacsinszky 6-2 6-1.
The fifth seed was barely tested by a player ranked 80 places below her and won 82 percent of points on her first serve to set up a meeting with American Alison Riske, a 7-5 6-2 winner over Italy's Camila Giorgi.
British involvement in the women's draw was brought to an end by Angelique Kerber, who overcame a tough test from Heather Watson to progress 6-2 5-7 6-1.
Kerber's quality shone through in the decider as the ninth seed booked a clash with 2013 semi-finalist Kirsten Flipkens following the Belgian's 6-2 6-1 hammering of Lourdes Dominguez Lino of Spain.
German Kerber is joined in the last 32 by compatriot and 2013 finalist Sabine Lisicki.
Lisicki racked up 29 winners in beating Czech Karolina Pliskova 6-3 7-5, however, the world number 19 faces a difficult encounter with Serbia's Ana Ivanovic in the third round.
Ivanovic - a winner at the Aegon Classic in Birmingham in the lead up to the tournament - continued her good form on grass by crushing Zheng Jie of China 6-4 6-0.
More German success came courtesy of Andrea Petkovic, with the 20th seed surviving a scare against Romania's Irina-Camelia Begu to advance 6-4 3-6 6-1.
Petkovic's triumph sets up an enticing match with Canadian 13th seed Eugenie Bouchard, who demonstrated the ability that led her to the last four of the Australian Open and French Open earlier this year in a 7-5 6-1 triumph over Spain's Silvia Soler-Espinosa.
The only shock of the day came as another Spaniard, Carla Suarez Navarro, suffered a 7-6 (14-12) 5-7 6-2 loss to Zarina Diyas of Kazakhstan in a mammoth encounter that lasted two hours and 46 minutes.
There was better news for Madison Keys, though, the promising American - a winner at the Aegon International at Eastbourne in June - overcoming the Czech Republic's Klara Koukalova 7-5 6-7 (3-7) 6-2.
Vera Zvonareva and Yaroslava Shvedova also won through, downing Donna Vekic and Kaia Kanepi respectively.