The Spaniard lost the opening set, but then raced through the second and was 4-6 6-0 4-1 ahead when her fifth-seeded opponent called it a day.
Niculescu's retirement came hot on the heels of that of her compatriot Alexandra Dulgheru.
The qualifier was 6-3 5-2 down to Czech third seed Klara Zakopalova when she withdrew.
Navarro and Zakopalova will face off in the semi-finals.
The other last-four clash will be between second seed Garbine Muguruza of Spain and Kazakhstan's Yaroslava Shvedova.
Muguruza battled past Belgian qualifier Alison Van Uytvanck in three sets, eventually winning in three sets 6-2 6-7 (7/9) 6-3, while Shvedova saw off a third Romanian, fifth seed Monica Niculescu, 6-3 6-3.