Synthesis protocols for anisotropic CuInX2 (X = S, Se, Te)-based heteronanocrystals (HNCs) are scarce due to the difficulty in balancing the reactivities of multiple precursors and the high solid-state diffusion rates of the cations involved in the CuInX2 lattice. In this work, we report a multistep seeded growth synthesis protocol that yields colloidal wurtzite CuInS2/ZnS dot core/rod shell HNCs with photoluminescence in the NIR (∼800 nm). The wurtzite CuInS2 NCs used as seeds are obtained by topotactic partial Cu+ for In3+ cation exchange in template Cu2- xS NCs. The seed NCs are injected in a hot solution of zinc oleate and hexadecylamine in octadecene, 20 s after the injection of sulfur in octadecene. This results in heteroepitaxial growth of wurtzite ZnS primarily on the Sulfur-terminated polar facet of the CuInS2 seed NCs, the other facets being overcoated only by a thin (∼1 monolayer) shell. The fast (∼21 nm/min) asymmetric axial growth of the nanorod proceeds by addition of [ZnS] monomer units, so that the polarity of the terminal (002) facet is preserved throughout the growth. The delayed injection of the CuInS2 seed NCs is crucial to allow the concentration of [ZnS] monomers to build up, thereby maximizing the anisotropic heteroepitaxial growth rates while minimizing the rates of competing processes (etching, cation exchange, alloying). Nevertheless, a mild etching still occurred, likely prior to the onset of heteroepitaxial overgrowth, shrinking the core size from 5.5 to ∼4 nm. The insights provided by this work open up new possibilities in designing multifunctional Cu-chalcogenide based colloidal heteronanocrystals.