Genetic variation in dispersal ability may result in the spatial sorting of alleles during range expansion. Recent theory suggests that spatial sorting can favour the rapid evolution of life history traits at expanding fronts, and therefore modify the ecological dynamics of range expansion. Here we test this prediction by disrupting spatial sorting in replicated invasions of the bean beetleﾠCallosobruchus maculatusﾠacross homogeneous experimental landscapes. We show that spatial sorting promotes rapid evolution of dispersal distance, which increases the speed and variability of replicated invasions: after 10 generations of range expansion, invasions subject to spatial sorting spread 8.9% farther and exhibit 41-fold more variable spread dynamics relative to invasions in which spatial sorting is suppressed. Correspondingly, descendants from spatially evolving invasions exhibit greater mean and variance in dispersal distance. Our results reveal an important role for rapid evolution during invasion, even in the absence of environmental filters, and argue for evolutionarily informed forecasts of invasive spread by exotic species or climate change migration by native species.