We demonstrate a new approach for synthesizing Ag-ZnO heterogeneous nanostructures in which single-crystalline ZnO nanorods were selectively grown on {111} rather than {100} facets of single-crystalline Ag truncated nanocubes. We have identified the fine structure of the Ag-ZnO heterostructures and proposed a mechanism indicating that structure match plays a critically important role in this type of facet-selective growth. These heterogeneous nanostructures are of special interest and have potential applications in electrical contacts, functional devices, biological sensors, and catalysis.