When ecological and evolutionary dynamics occur on comparable timescales, persistence of the ensuing eco-evolutionary dynamics requires both ecological and evolutionary stability. This unites key questions in ecology and evolution: How do species coexist, and what maintains genetic variation in a population? In this work, we investigated a host-parasitoid system in which pea aphid hosts rapidly evolve resistance to Aphidius ervi parasitoids. Field data and mathematical simulations showed that heterogeneity in parasitoid dispersal can generate variation in parasitism-mediated selection on hosts through time and space. Experiments showed how evolutionary trade-offs plus moderate host dispersal across this selection mosaic cause host-parasitoid coexistence and maintenance of genetic variation in host resistance. Our results show how dispersal can stabilize both the ecological and evolutionary components of eco-evolutionary dynamics.