In stochastic resonance, a periodically forced Brownian particle in a double-well potential jumps between minima at rare increments, the prediction of which pose a major theoretical challenge. Here, we use a path-integral method to predict these transitions by determining the most probable (or "optimal") space-time path of a particle. We characterize the optimal path using a direct comparison principle between the Langevin and Hamiltonian dynamical descriptions, allowing us to express the jump condition in terms of the accumulation of noise around the stable periodic path. In consequence, as a system approaches a rare event these fluctuations approach one of the deterministic minimizers, thereby providing a precursor for predicting the stochastic transition. We demonstrate the method numerically, which allows us to determine whether a state is following a stable periodic path or will experience an incipient jump. The vast range of systems that exhibit stochastic resonance behavior insures broad relevance of our framework, which allows one to extract precursor fluctuations from data.