Metallic nanostructures support extreme localization and enhancement of optical fields via surface-plasmon (SP) resonances. Although SP are associated with giant enhancements of nonlinear phenomena such as second-harmonic generation (SHG), the role of SP in the process, whether as a field-enhancing catalyst or as a quasiparticle converted in the interaction, has remained experimentally elusive. We demonstrate how k-space spectroscopy can distinguish between the plasmonic and photonic SHG processes that occur in a metal nanofilm when it is optically driven via the Kretschmann geometry. The results revealed a nonlinear interaction where two SP annihilate to create a second-harmonic photon. This knowledge has implications for realizing the inverse process, plasmonic parametric down-conversion, which could act as a coherent source of entangled SP pairs.