Sharapova posted consecutive 6-0, 6-0 wins in the first two rounds and ran her gamewinning streak to 28 before losing her first of the tournament. Still she went on to a 6-1, 6-2 victory over the No. 25-seeded Williams.
After dropping that game, Sharapova won the next five for a 3-0 lead in the second set. Williams staved off elimination by breaking Sharapova's serve to get to 2-5 but two games later Sharapova was through the round.
She won 60 percent of the points in the match, including 56 percent when Williams, who had 26 unforced errors, served. That allowed Sharapova to pile up five breaks in eight games.
Only one unseeded player advanced to the fourth round in the lower half of the women's draw. Kirsten Flipkens beat Valeria Savinykh, also unseeded, 6-2, 4-6, 6-3 behind six breaks. Flipkens draws Sharapova in the next round.
Fourth-seeded Agnieszka Radwanska had little trouble getting by Heather Watson 6-3, 6-1 in her Friday match. Radwanska had five aces, with no double faults, and only 13 unforced errors. Radwanska is 12-0 in matches and hasn't dropped a set in 2013.
In addition to the Sharapova-Flipkens pairing, other fourth-round matches have Radwanska playing Ivanovic, Kerber going against Makarova and Li facing Goerges.
Biologists detail four new deep-sea 'killer sponges'
Pistorius testifies he didn't consciously pull trigger when he shot girlfriend