Cirstea, who had won all four previous matches against Voegele, held serve only once. Her service game was woeful, while Voegele got away with making only a third of her first serves, and dropping serve only once.
The Romanian, who enjoyed a career-best year in 2013 to rank 22, has reached only two quarterfinals this year, and none since February. Because of a right shoulder injury, this was Cirstea's second tournament in two months.
Defending champion Eliva Svitolina of Ukraine, seeded No. 2, beat Silvia Soler-Espinosa of Spain 7-5, 6-2 and will meet Pauline Parmentier of France in the quarters.
Former French Open champion Francesca Schiavone won 6-2, 7-6 (2) against Julia Glushko of Israel, who converted only two of eight break points, and lined up Kristina Mladenovic for the second time this year after the Frenchwoman overcame Donna Vekic of Croatia 2-6, 6-3, 6-0. Bojana Jovanovski of Serbia plays Misa Eguchi of Japan in the other quarter.