We generalize Yekutieli-Zhang's noncommutative Serre Duality Theorem to the setting of noncommutative spaces associated to dg-algebras. As an application, we establish some finiteness properties of derived global sections over such noncommutative spaces. Along the way, we generalize Yekutieli's notion of a balanced dualizing complex to the setting of dg-algebras and establish some cases in which they exist.