Correlations between the energies of elementary steps limit the rates of thermally catalysed reactions at surfaces. Here, we show how these limitations can be circumvented in ammonia synthesis by coupling catalysts to a non-thermal plasma. We postulate that plasma-induced vibrational excitations in N2 decrease dissociation barriers without influencing subsequent reaction steps. We develop a density-functional-theory-based microkinetic model to incorporate this effect, and parameterize the model using N2 vibrational excitations observed in a dielectric-barrier-discharge plasma. We predict plasma enhancement to be particularly great on metals that bind nitrogen too weakly to be active thermally. Ammonia synthesis rates observed in a dielectric-barrier-discharge plasma reactor are consistent with predicted enhancements and predicted changes in the optimal metal catalyst. The results provide guidance for optimizing catalysts for application with plasmas.