Top seed and world number one Williams, who is bidding to hold all four majors at the same time for the second time in her career -- 'the Serena Slam' -- has a 17-2 record over Sharapova.
The Russian's last win over the American was in the 2004 Wimbledon final.
Serena could meet sister Venus, a four-time champion, in the fourth round.
Second seed and defending champion Petra Kvitova would potentially meet Simona Halep in the semi-finals.