Mixed-dimensional heterostructures (MDHs), which combine nanomaterials of different dimensionalities deliver on the promise to bypass intrinsic limitations of a given low-dimensional material. Here, a strategy to engineer MDHs between two low-dimensional materials by curvature-complementary self-assembly is described. CdSe nanotubes rolled from 2D nanosheets and 1D CdSe nanorods, with negative and positive curvatures, respectively, are selected to illustrate complementary curvature self-assembly. The assembly process, optical, and photoelectrical properties of the CdSe MDHs are thoroughly investigated. Several remarkable features of CdSe MDHs, including increased light absorption, efficient charge separation, and appropriate bandgap structure are confirmed. The MDHs significantly alleviate the sluggish kinetics of electron transfer in the quantum sized CdSe subunits (onset potential of 0.21V vs RHE for MDHs; 0.4V lower than their low-dimensional building blocks), while the spatial nano-confinement effect in the CdSe MDHs also assists the interfacial reaction kinetics to render them ideal photocatalysts for benzylamine oxidation (conversion >99% in 4h with a two times higher rate than simple mixtures). The results highlight opportunities for building MDHs from low-dimensional building blocks with curvature-complementary features and expand the application spectrum of low dimensional materials in artificial photosynthesis.