Nonlinear molecular interactions with optical fields produce intriguing optical phenomena and applications ranging from color generation to biomedical imaging and sensing. The nonlinear cross-section of dielectric materials is low and therefore for effective utilisation, the optical fields need to be amplified. Here, we demonstrate that two-photon absorption can be enhanced by 108 inside individual plasmonic nanocavities containing emitters sandwiched between a gold nanoparticle and a gold film. This enhancement results from the high field strengths confined in the nanogap, thus enhancing nonlinear interactions with the emitters. We further investigate the parameters that determine the enhancement including the cavity spectral position and excitation wavelength. Moreover, the Purcell effect drastically reduces the emission lifetime from 520 ns to <200 ps, turning inefficient phosphorescent emitters into an ultrafast light source. Our results provide an understanding of enhanced two-photon-excited emission, allowing for optimization of efficient nonlinear light-matter interactions at the nanoscale.