Trophic relationships between invasive species in multiply invaded ecosystems may reduce food limitation relative to more pristine ecosystems and increase resilience to control. Here, we consider whether invasive predatory American mink Neovison vison are trophically subsidized by invasive crayfish. We collated data from the literature on density and home range size of mink populations in relation to the prevalence of crayfish in the diet of mink. We then tested the hypothesis that populations of an invasive predator reach higher densities and are more resilient to lethal control when they have access to super-abundant non-native prey, even in the absence of changes in density dependence, hence compensatory capacity. We found a strong positive relationship between the proportion of crayfish in mink diet and mink population density, and a negative relationship between the proportion of crayfish in mink diet and mink home range size, with crayfish contribution to mink diet reflecting their abundance in the ecosystem. We then explored the consequence of elevated mink density by simulating a hypothetical eradication program with a constant harvest in a Ricker model. We found that mink populations were more resilient to harvest in the presence of crayfish. As a result, the simulated number of mink harvested to achieve eradication increased by 500% in the presence of abundant crayfish if carrying capacity increased by 630%. This led to a threefold increase in time to eradication under a constant harvest and an approximately 20-fold increase in the cumulative management cost. Our results add to evidence of inter-specific positive interactions involving invasive species, and our simple model illustrates how this increases management cost.