Although predators affect prey both via consumption and by changing prey migration behavior, the interplay between these two effects is rarely incorporated into spatial models of predator–prey dynamics and competition among prey. We develop a model where generalist predators have consumptive effects (i.e., altering the likelihood of local prey extinction) as well as nonconsumptive effects (altering the likelihood of colonization) on spatially separated prey populations (metapopulations). We then extend this model to explore the effects of predators on competition among prey. We find that generalist predators can promote persistence of prey metapopulations by promoting prey colonization, but predators can also hasten system-wide extinction by either increasing local extinction or reducing prey migration. By altering rates of prey migration, predators in one location can exert remote control over prey dynamics in another location via predator-mediated changes in prey flux. Thus, the effect of predators may extend well beyond the proportion of patches they visit. In the context of prey metacommunities, predator-mediated shifts in prey migration and mortality can shift the competition–colonization trade-off among competing prey, leading to changes in the prey community as well as changes in the susceptibility of prey species to habitat loss. Consequently, native prey communities may be susceptible to invasion not only by exotic prey species that experience reduced amounts of mortality from resident predators, but also by exotic prey species that exhibit strong dispersal in response to generalist native predators. Ultimately, our work suggests that the consumptive and nonconsumptive effects of generalist predators may have strong, yet potentially cryptic, effects on competing prey capable of mediating coexistence, fostering invasion, and interacting with anthropogenic habitat alteration.