Scheepers, Peer advance to Budapest quarterfinals
"I'm happy to have made the transition to clay from grass fairly smoothly,'' said Scheepers, the sixth seed. "Petra is such a good player, so I knew I had to take my chances when I got them.''
Scheepers' next opponent will be Danka Kovinic of Montenegro, who beat Valeria Solovyeva of Russia 6-1, 3-6, 6-1.
Peer, who won her last WTA tournament in 2009, will face Romania's Alexandra Cadantu.
Cadantu defeated Andrea Hlavackova of the Czech Republic, who retired due to cramping with the Romanian leading 4-6, 7-5, 4-0.