We report the observation of a resonant enhancement of spin pumping induced by magnon-phonon coupling at room temperature. We show that the spin pumping driven by microwave parametric excitation is enhanced, compared to its purely magnonic value, when the microwave excites dipole-exchange magnons in the proximity of the intersection of the uncoupled magnon and phonon dispersions. This observation is consistent with a model of the spin pumping driven by hybridized magnon-phonon modes, magnon polarons, where the spin-pumping efficiency depends on the relative scattering strengths of the magnons and phonons in a magnetic insulator.