Begu defeated second-seeded Roberta Vinci 6-4, 6-3, leaving Vinci the only seeded player not to advance to the tournament quarterfinals.
Vinci beat Begu on Sunday in the finals of a tournament in Hungary in their only other career meeting. But on Thursday Begu was able to pull off four breaks in nine Vinci service games to get the upset.
Third-seeded Sara Errani advanced with a 7-5, 6-1 win over Pauline Parmentier while No. 4-seeded Klara Zakopalova beat Ani Mijacika 7-5, 4-6, 6-3 and fifth-seeded Anabel Medina Garrigues was a 6-1, 7-5 winner over Lara Arruabarrena-Vecino.
Begu will go against Medina-Garrigues in Friday's quarterfinals and Errani will play eighth-seeded Petra Cetkovska. Zakopalova is to play No. 7-seeded Polona Hercog while top-seeded Flavia Pennetta takes on sixth-seeded Tsvetana Pironkova.