Natural populations of hosts and their enemies are often spatially structured, with patches that vary in the strength of reciprocal selection, so-called coevolutionary hotspots and coldspots with strong or weak reciprocal selection, respectively. Theory predicts that dispersal from hotspots should intensify coevolution in coldspots, whereas dispersal from coldspots should weaken coevolution in hotspots; however, there have been few empirical tests. We addressed this using paired populations of the bacterium Pseudomonas fluorescens and the phage SBW25Phi2 linked by one-way dispersal. Within each population, the strength of reciprocal selection was manipulated by altering the bacteria-phage encounter rate, which changes the rate of coevolution without affecting environmental productivity. We observed that dispersal from hotspots accelerated coevolution in coldspots, while dispersal from coldspots decelerated coevolution in hotspots. These results confirm theoretical predictions and suggest that source populations can act as coevolutionary "pacemakers" for recipient populations, overriding local conditions.