"She played really well in the first set," the third-seeded Petkovic said in a courtside interview.
"She has a tremendous serve for her height. It's really one of the best serves that I had to return on the WTA tour."
Hradecka's victory continued a string of upsets at the tournament, which has had several early exits of top seeds including Canada's Eugenie Bouchard and Russian Ekaterina Makarova.
A decorated doubles player, but ranked only 110th in singles, Hradecka beat fourth seed Errani 6-2 6-4, her third victory against a seeded player on her way to the semi-finals.
Hradecka will face seventh-seed Madison Keys, who overpowered qualifier Lauren Davis 6-2 6-2.
(Reporting by Cameron French; Editing by Greg Stutchbury)
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