Cirstea defeated Alison Riske 6-3, 6-4 by going 4-for-4 in break opportunities. She had a pair of breaks in each set to more than offset losing two games on serve.
Cirstea won nearly half (25-of-51) of the points off Riske's serve.
Fourth-seeded Ekaterina Makarova routed Russian countrywoman Vera Zvonareva 6-0, 6-2 in a brisk 63 minutes. Makarova won nearly two-thirds of the points in the match and finished off five of her six break chances.
Karolina Pliskova gained a spot in the quarterfinals opposite Cirstea with a 4-6, 6-3, 6-4 win over Alla Kudryavtseva. The match was tight -- Pliskova finished with an 89-86 edge in points won -- but Pliskova got the only break of the second set and added two more in the third for the win.
The tournament lost its top two seeds to injury with No. 1-seeded Sabine Lisicki withdrawing due to a shoulder injury and second-seeded Svetlana Kuznetsova out after hurting her left hip. Those moves allowed Andrea Hlavackova and Julia Goerges to advance to the quarterfinals with walkovers.
Swim Week Miami Beach 2014 [PHOTOS]