We have devised a novel importance sampling method for nonequilibrium processes. Like transition path sampling, the method employs a Monte Carlo procedure to confine or bias the search through trajectory space. In this way, molecular dynamics trajectories consistent with the nonequilibrium dynamics of interest are generated efficiently. Using results of this sampling, we demonstrate that statistics of the energy gap between a solute's electronic states are Gaussian throughout the dynamics of nonequilibrium solvation in water. However, these statistics do change in time, reflecting linear response that is nonstationary. Discrepancies observed between the dynamics of nonequilibrium relaxation and of equilibrium fluctuations are thus explained. We analyze a simple Gaussian field theory that accounts fur this nonstationary response.