Spain's Suarez-Navarro overcame a brief rain delay in the second set to get past the Netherlands' Kiki Bertens 6-3, 7-6 (7-2).
Her next opponent will be Romanian No. 5 seed Niculescu, who took down qualifier Danka Kovinic of Montenegro 6-3, 6-1.
Czech Klara Zakopalova, coming off a runner-up showing in last week's Rio de Janeiro event, also moved on to the quarters with a 6-3, 6-3 drubbing of French qualifier Alize Lim.
Next up for her will be Romanian Alexandra Dulgheru, winner of a 7-5, 6-2 decision over Brazil's Teliana Pereira.
Also Wednesday, eighth-seeded Argentine Paula Ormaechea tumbled to Belgian qualifier Alison Van Uytvanck in a 6-2, 6-2 upset.