Cabeza Candela, a qualifier who had the backing of the home crowd, handled Dulgheru 7-5, 6-3, and now goes on to face Czech Lucie Hradecka in the quarterfinals.
Two other seeded players, however, had better luck Wednesday in Barcelona.
Fifth-seeded Sara Errani dispatched fellow Italian Maria Elena Camerin 6-4, 6-1. Sixth-seeded Roberta Vinci, also of Italy, bested Yaroslava Shvedova of Kazakhstan 6-1, 6-4.
Vinci is seeking to compete in her third straight Barcelona final after winning the crown in 2009. She will play France's Virginie Razzano in Thursday's quarterfinals while Errani will face fellow Italian Alberta Brianti.
Other Barcelona winners included Slovenian Polona Hercog and Spain's Laura Pous-Tio.
Swim Week Miami Beach 2014 [PHOTOS]