Slovakia's Hantuchova dropped the first set against Dutchwoman Arantxa Rus before rebounding for a 3-6, 6-4, 6-1 victory. Germany's Petkovic rallied for a 4-6, 6-2, 6-1 win over Spanish qualifier Garbine Muguruza.
Petkovic, who has been out most of the 2012 season with knee and ankle injuries, will next meet third-seeded former world No. 1 Jelena Jankovic of Serbia. Hantuchova will take on Belgian Kirsten Flipkens.
Advancing to the quarterfinals were Spain's Lourdes Dominguez Lino, who dispatched Slovak Magdalena Rybarikova 6-2, 6-3, and Czech Lucie Hradecka, who posted a 6-1, 6-1 rout of German qualifier Annika Beck.
Also Wednesday, Briton Anne Keothavong and Russia's Ksenia Pervak each reached the second round with Day 3 wins.
Celebrity Couples of 2014 [PHOTOS]