We study second-harmonic generation from single CdTe/CdS core/shell rod-on-dot nanocrystals with different geometrical parameters, which allow to fine tune the nonlinear properties of the nanostructure. These hybrid semiconductor-semiconductor nanoparticles exhibit extremely strong and stable second-harmonic emission, although the size of CdTe core is still within the strong quantum confinement regime. The orientation sensitive polarization response is analyzed by means of a pointwise additive model of the third-order tensors associated to the nanoparticle components. These findings prove that engineering of semiconducting complex heterostructures at the single nanoparticle scale can lead to extremely bright nanometric nonlinear light sources.