Errani, the tournament's No. 5-seed, defeated Alberta Brianti 6-2, 6-3 with six breaks in Brianti's nine service games. Errani lost her own serve twice but still only dropped 16 points on serve.
Hradecka eliminated qualifier Estrella Cabeza Candela, who was coming off an upset of second-seeded Alexandra Dulgheru, 6-4, 6-4. There were a total of 10 service breaks in the 20-game match. Even with four lost service games, Hradecka won 60 percent of the points on serve.
Errani will face Hradecka in Friday's semifinals. The two have only played once before, in a 2010 Fed Cup match that Errani won in straight sets.
The other semifinal is to be determined. While No. 6-seeded Roberta Vinci defeated Virginie Razzano 6-4, 6-1, taking 59 percent of the points in the process, the fourth quarterfinal Thursday between Polona Hercog and Laura Pous-Tio was suspended because of rain.
That match, in which Hercog is ahead 6-5 in the first set with Pous-Tio serving, will be completed Friday before the semifinal round.
Celebrity Families of 2014 [PHOTOS]