Time-dependent nonlinear media, such as rapidly generated plasmas produced via laser ionization of gases, can increase the energy of individual laser photons and generate tunable high-order harmonic pulses. This phenomenon, known as photon acceleration, has traditionally required extreme-intensity laser pulses and macroscopic propagation lengths. Here, we report on a novel nonlinear material-an ultrathin semiconductor metasurface-that exhibits efficient photon acceleration at low intensities. We observe a signature nonlinear manifestation of photon acceleration: third-harmonic generation of near-infrared photons with tunable frequencies reaching up to ≈3.1ω. A simple time-dependent coupled-mode theory, found to be in good agreement with experimental results, is utilized to predict a new path towards nonlinear radiation sources that combine resonant upconversion with broadband operation.