Invasive alien species (IAS) are identified as a major threat to biodiversity and ecosystem services. While early detection and control programs to avoid establishments of new alien species can be very cost-effective, control costs for well-established species can be enormous. Many of these well-established species constitute severe or high ecological impact and are thus likely to be included in control programs. However, due to limited funds, we need to prioritize which species to control according to the gains in ecological status and human well-being compared to the costs. Benefit-Cost Analysis (BCA) provides such a tool but has been hampered by the difficulties in assessing the overall social benefits on the same monetary scale as the control costs. In order to overcome this obstacle, we combine a non-monetary benefit assessment tool with the ecosystem service framework to create a benefit assessment in line with the welfare economic underpinnings of BCA. Our simplified BCA prioritization tool enables us to conduct rapid and cheap appraisals of large numbers of invasive species that the Norwegian Biodiversity Information Centre has found to cause negative ecological impacts. We demonstrate this application on 30 well-established invasive alien vascular plant species in Norway. Social benefits are calculated and aggregated on a benefit point scale for six impact categories: four types of ecosystem services (supporting, provisioning, regulating and cultural), human health and infrastructure impacts. Total benefit points are then compared to the total control costs of programs aiming at eradicating individual IAS across Norway or in selected vulnerable ecosystems. Although there are uncertainties with regards to IAS population size, benefits assessment and control program effectiveness and costs; our simplified BCA tool identified six species associated with robust low cost-benefit ratios in terms of control costs (in million USD) per benefit point. As a large share of public funds for eradication of IAS is currently spent on control programs for other plant species, we recommend that the environmental authorities at all levels use our BCA prioritization tool to increase the social benefits of their limited IAS control budgets. In order to maximize the net social benefits of IAS control programs, environmental valuation studies of their ecosystem service benefits are needed.