The second-seeded Sharapova continued her strong run at Stade Roland Garros with a 6-2, 6-1 pasting of China's Peng Shuai -- her toughest match so far. She had previously breezed past Alexandra Cadantu and Ayumi Morita in dominating style.
Sharapova now goes on to face another unseeded foe, Klara Zakopalova of the Czech Republic, who made the fourth round by dumping 22nd-seeded Russian Anastasia Pavlyuchenkova, 6-3, 7-5.
Former French Open champion Schiavone, meanwhile, was upended by Varvara Lepchenko, an Uzbekistan-born American, who also beat Schiavone at the Madrid Open last month.
Lepchenko lost the first set but came back to post a 3-6, 6-3, 8-6 victory.
Defending champion Li Na of China rallied to beat American Christina McHale, overcoming 24 unforced errors in the first set to gut out a 3-6, 6-2, 6-1 victory.
Li will next face Yaroslava Shevova of Kazakhstan, who knocked off Spain's Carla Suarez Navarro Saturday 6-4, 7-5.
Also advancing Saturday was Wimbledon champ and No. 4 seed Petra Kvitova, who topped Russian Nina Bratchikova 6-2, 4-6, 6-1.