Invasive mammal eradications are increasingly attempted across large, complex landscapes. Sequentially controlled management zones can be at risk of reinvasion from adjacent uncontrolled areas, and managers must weigh the relative benefits of ensuring complete elimination from a zone or minimizing reinvasion risk. This is complicated in urban areas, where habitat heterogeneity and a lack of baseline ecological knowledge increase uncertainty. We applied a spatial agent‐based model to predict the reinvasion of a well‐studied species, the brushtail possum (Trichosurus vulpecula), across an urban area onto a peninsula that is the site of an elimination campaign in Aotearoa New Zealand. We represented fine‐scale urban habitat heterogeneity in a land cover layer and tested management scenarios that varied four factors: the density of possums remaining following an elimination attempt, the maintenance trap density on the peninsula, and effort expended toward preventing reinvasion by means of a high‐density trap buffer at the peninsula isthmus or control of the source population adjacent to the peninsula. We found that achieving complete elimination on the peninsula was crucial to avoid rapid repopulation. The urban isthmus was predicted to act as a landscape barrier and restrict immigration onto the peninsula, but reliance on this barrier alone would fail to prevent repopulation. In combination, complete elimination, buffer zone, and source population control could reduce the probability of possum repopulation to near zero. Our findings support urban landscape barriers as one tool for sequential invasive mammal elimination but reaffirm that novel methods to expose residual individuals to control will be necessary to secure elimination in management zones. Work to characterize the urban ecology of many invasive mammals is still needed.