Hetero-epitaxial growth along three-dimensional (3D) interfaces from materials with an intrinsic large lattice mismatch is a key challenge today. In this work we report, for the first time, the controlled synthesis of vertically aligned ZnO/ZnS core/shell nanorod arrays composed of single crystalline wurtzite (WZ) ZnS conformally grown on ZnO rods along 3D interfaces through a simple two-step thermal evaporation method. Structural characterization reveals a "(01-10)(ZnO)//(01-10)(ZnS) and [0001](ZnO)//[0001](ZnS)" epitaxial relationship between the ZnO core and the ZnS shell. It is exciting that arrays of single crystalline hollow ZnS nanotubes are also innovatively obtained by simply etching away the inner ZnO cores. On the basis of systematic structural analysis, a rational growth mechanism for the formation of hetero-epitaxial core/shell nanorods is proposed. Optical properties are also investigated via cathodoluminescence and photoluminescence measurements. Remarkably, the synthesized ZnO/ZnS core/shell heterostructures exhibit a greatly reduced ultraviolet emission and dramatically enhanced green emission compared to the pure ZnO nanorods. The present single-crystalline heterostructure and hollow nanotube arrays are envisaged to be highly promising for applications in novel nanoscale optoelectronic devices, such as UV-A photodetectors, lasers, solar cells, and nanogenerators.