Three-dimensional (3D) nanoarchitectures can offer enhanced material properties, such as large surface areas that amplify the structures' interaction with environments making them useful for various sensing applications. Self-assembled block copolymers (BCPs) can readily generate various 3D nanomorphologies, but their conversion to useful inorganic materials remains one of the critical challenges against the practical application of self-assembled BCPs. This work reports the vapor-phase infiltration synthesis of optoelectrically active, 3D ZnO nanomesh architectures by combining hierarchical successive stacking of self-assembled, lamellar-phase polystyrene-block-poly(2-vinylpyridine) (PS-b-P2VP) BCP thin films and a modified block-selective vapor-phase material infiltration protocol. The 3D ZnO nanomesh exhibits optoelectrical functionality, featuring stack-layer-number-dependent electrical conductance resembling the percolative transport originating from the intrinsic morphological network connectivity of the lamellar BCP pattern with symmetric block ratio. The results not only illustrate the first demonstration of electrical functionality based on the ZnO nanoarchitecture directly generated by the infiltration synthesis in self-assembled BCP thin films but also present a new, large-area scalable, metal oxide thin film nanoarchitecture fabrication method utilizing industry-compatible polymer solution coating and atomic layer deposition. Given the large surface area, three-dimensional porosity, and readily scalable fabrication procedures, the generated ZnO nanomesh promises potential applications as an efficient active medium in chemical and optical sensors.