An original plasmonic nano-Ag/SiNx substrate was elaborated to strongly enhance the nonlinear response of SiC NPs for the first time. A plasmon-induced two order of magnitude increase of second-harmonic generation and two-photon excited photoluminescence was experimentally achieved. The measured enhancement factors were correlated with local field intensities theoretically estimated by finite-difference time-domain calculations. The obtained plasmon-enhanced nonlinear response of the SiC nanostructures make them promising in nonlinear optics applications.