We revisit the exciton mechanism of superconductivity in the framework of microcavity physics, replacing virtual excitons as a binding agent of Cooper pairs by excitations of an exciton-polariton Bose-Einstein condensate. We consider a model microcavity where a quantum well with a two-dimensional electron gas is sandwiched between two undoped quantum wells, where a polariton condensate is formed. We show that the critical temperature for superconductivity dramatically increases with the condensate population, opening a new route towards high-temperature superconductivity.