Knapp dispatched Dulgheru 6-2, 6-2 on the red clay court at the Centro de Alto Rendimiento.
Other seeded players fared better on Day 2 in Bogota.
No. 3 seed Romina Oprandi of Switzerland moved on with a 6-2, 6-2 whipping of Romanian Alexandra Cadantu, and fifth-seeded Gisela Dulko of Argentina got past German Kathrin Woerle 1-6, 6-2, 6-4.
Also Tuesday, No. 7 seed and reigning Bogota champion Lourdes Dominguez Lino of Spain took care of Canadian Sharon Fichman 6-2, 6-2.
Dominguez Lino won the Bogota event in 2006 and was the runner-up in 2005.
Swim Week Miami Beach 2014 [PHOTOS]