Her reward will be a matchup with France's Marion Bartoli, who posted a convincing victory over Weingartner in the final round of qualifying.
"This has never happened to me before," Bartoli said. "You think when you have beaten a player, you will not play them again. But here we are."
Weingartner made the main draw when defending champion Anna Pistolesi pulled out due to heat exhaustion. She led France's Nathalie Dechy, 5-0, in the first round when the top seed retired with a quadriceps strain.
The 98th-ranked woman in the world, Weingartner advanced the conventional way Wednesday, moving within one match of her third career semifinal appearance.
Bartoli outlasted seventh seed Laura Granville of the United States, 7-5, 4-6, 6-4, to set up a rematch with Weingartner. She opened the tournament with a straight-sets victory over Meilen Tu of the United States.
"I am excited to be in the quarterfinals but not so much surprised," said the 18-year-old Bartoli, who is ranked 104th. "I beat some good players last year and I am very confident against these girls."
Second seed Meghann Shaughnessy advanced to the quarterfinals with a 6-2, 6-3 triumph over Conchita Martinez Granados of Spain. Shaughnessy next faces eighth seed Magui Serna of Spain.
Emilie Loit also sealed a spot in the quarterfinals, defeating Angelique Widjaja of Indonesia, 6-4, 6-4. Loit's next foe will be Adriana Serra-Zanetti of Italy.