The use of single molecule magnets in mainstream electronics requires their magnetic moment to be stable over long times. One can achieve such a goal by designing compounds with spin-reversal barriers exceeding room temperature, namely with large uniaxial anisotropies. Such strategy, however, has been defeated by several recent experiments demonstrating under-barrier relaxation at high temperature, a behaviour today unexplained. Here we propose spin-phonon coupling to be responsible for such anomaly. With a combination of electronic structure theory and master equations we show that, in the presence of phonon dissipation, the relevant energy scale for the spin relaxation is given by the lower-lying phonon modes interacting with the local spins. These open a channel for spin reversal at energies lower than that set by the magnetic anisotropy, producing fast under-barrier spin relaxation. Our findings rationalize a significant body of experimental work and suggest a possible strategy for engineering room temperature single molecule magnets.