Given the limited funds available for the management of invasive alien species (IASs), there is a need to design cost-effective strategies to prioritize their control. In this paper, we propose a cost-benefit optimization framework that incorporates the spatially explicit costs and benefits of invasion control, as well as the spatial invasion dynamics. Our framework offers a simple yet operational priority-setting criterion for the spatially explicit management of IASs under budget constraints. We applied this criterion to the control of the invasion of primrose willow (genus Ludwigia) in a protected area in France. Using a unique geographic information system panel dataset on control costs and invasion levels through space for a 20-year period, we estimated the costs of invasion control and a spatial econometric model of primrose willow invasion dynamics. Next, we used a field choice experiment to estimate the spatially explicit benefits of invasion control. Applying our priority criterion, we show that, unlike the current management strategy that controls the invasion in a spatially homogeneous manner, the criterion recommends targeted control on heavily invaded areas that are highly valued by users. We also show that the returns on investment are high, justifying the need to increase the allocated budgets and to treat the invasion more drastically. We conclude with policy recommendations and possible extensions, including the development of operational cost-benefit decision-support tools to assist local decision-makers in setting management priorities.