The structure sensitivity of acetylene hydrogenation was studied over size‐controlled cubic and octahedral Pd nanocrystals (NCs) supported on ZnO and SiO2. Acetylene hydrogenation was found to be structure sensitive [with Pd(1 1 1) in octahedra being more active than Pd(1 0 0) in cubes]. However, the response was found to vary depending on the redox properties of the support. The catalytically active and selective palladium carbide (PdCx) phase was readily formed on the SiO2‐supported Pd NCs (much faster on cubes than on octahedra), whereas a markedly less active PdZn phase was preferentially formed on the ZnO‐supported Pd nanocrystals. Here we show that the structure sensitivity of a chemical reaction is a complex phenomenon that originates from the reconstruction of the active phase in response to the reactive environment, which is ultimately determined by the support used.