In this study, a facile solution approach was developed for the synthesis of a series of core-shell structured Ag@CuO nanocrystals of various shapes including triangles, spheres, and cubes with well-defined stable heterojunctions. The electrooxidation of dopamine (DA), uric acid (UA), guanine (G), and adenine (A) using these hybrids revealed morphology-dependent sensing properties, with activities and accumulation ability following the order, triangular Ag@CuO > spherical Ag@CuO > cubic Ag@CuO. Further, we constructed a novel graphene oxide (GO) nanosheet-reinforced triangular Ag@CuO ternary hetero-nanostructure. Such a hybrid with a three-dimensional interconnected hierarchical architecture is suitable for catalysis, since it not only leads to improved interfacial electron transfer, but also readily exposes the highly catalytic Ag@CuO to the reactants. Therefore, more enhanced electrochemical activities were observed for the oxidation of DA, UA, G, and A. This study provides an efficient way to synthesize morphology-controlled Ag@CuO heterogeneous catalysts for the fabrication of potential biosensors, and also opens up attractive avenues in the design of multifunctional ternary noble metal-semiconductor-carbon hybrids.