The Italian sixth seed, the only seed left in the competition, won 7-6 (7/4) 6-1 to set up a meeting with Spain's Lourdes Dominguez Lino.
The Spaniard recovered from going a set down to fight back and defeat Luxembourg's Mandy Minella 2-6 6-0 6-1.
Schiavone, the former French Open champion now ranked 48th in the world, and Scheepers had one break each in the first set, but the experienced 32-year-old held her nerve in the tie-break.
Schiavone then broke three times in the second set to seal victory in one hour 46 minutes.
Dominguez Lino looked to be heading out when she was broken three times in the opening set, but she broke three times herself in the next and saved the six break points she faced to level the match.
And the Spanish player broke three more times in the decider to clinch the win in one hour 48 minutes.