A new mechanism is presented which can reheat the Universe in non-oscillatory models of inflation, where the inflation period is followed by a period dominated by the kinetic density for the inflaton field (kination). The mechanism considers an auxiliary field non-minimally coupled to gravity. The auxiliary field is a spectator during inflation, rendered heavy by the non-minimal coupling to gravity. During kination however, the non-minimal coupling generates a tachyonic mass, which displaces the field, until its bare mass becomes important, leading to coherent oscillations. Then, the field decays into the radiation bath of the hot big bang. The model is generic and predictive, in that the resulting reheating temperature is a function only of the model parameters (masses and couplings) and not of initial conditions. It is shown that reheating can be very efficient also when considering only the Standard Model.