Top seed Misaki Doi's surprise exit has left the top half of the draw wide open and, despite an almighty struggle to cross the finishing line, Siniakova refused to let her own challenge be derailed.
Leading by a set and 5-2, Siniakova appeared to be cantering to victory. Chirico, though, refused to go down without a fight, breaking three times in the next five games to take the match the distance.
The deciding set followed a similar pattern, the Czech squandering a 5-3 lead before finally closing out a 6-4, 5-7, 7-6(3) victory after one minute shy of three hours on court.
Also advancing to the last eight were a couple more unseeded players, Varvara Lepchenko and Jana Cepelova. Lepchenko upset No.4 seed Johanna Larsson, 6-2, 3-6, 6-4, while Cepelova eased past qualifier Jang Su Jeong, 6-3, 6-1.
Osaka produced a clinical display to see off Anett Kontaveit, 6-0, 6-2, in under an hour, while Linette, last year's finalist, was every big as impressive in a 6-1, 6-0 win over Erika Sema. No.3 seed Yulia Putintseva was kept on court slightly longer, defeating Maria Sakkari, 6-4, 6-3.