Phase engineering of nanomaterials (PEN) enables the preparation of metal nanomaterials with unconventional phases that are different from their thermodynamically stable counterparts. These unconventional-phase nanomaterials can serve as templates to construct precisely controlled metallic heterostructures for wide applications. Nevertheless, how the unconventional phase of templates affects the nucleation and growth of secondary metals still requires systematic explorations. Here, two-dimensional (2D) square-like Au nanosheets with an unconventional 2H/face-centered cubic (fcc) heterophase, composing of two pairs of opposite edges with 2H/fcc heterophase and fcc phase, respectively, and two 2H/fcc heterophase basal planes, are prepared and then used as templates to grow one-dimensional (1D) Rh nanorods. The effect of different phases in different regions of the Au templates on the overgrowth of Rh nanorods has been systematically investigated. By tuning the reaction conditions, three types of 1D/2D Rh-Au heterostructures are prepared. In the type A heterostructure, Rh nanorods only grow on the fcc defects including stacking faults and/or twin boundaries (denoted as fcc-SF/T) and 2H phases in two 2H/fcc edges of the Au nanosheet. In the type B heterostructure, Rh nanorods grow on the fcc-SF/T and 2H phases in two 2H/fcc edges and two 2H/fcc basal planes of the Au nanosheet. In the type C heterostructure, Rh nanorods grow on four edges and two basal planes of the Au nanosheet. Furthermore, the type C heterostructure shows promising performance toward the electrochemical hydrogen evolution reaction (HER) in acidic media, which is among the best reported Rh-based and other noble-metal-based HER electrocatalysts.