Predicting the dynamics and impacts of multiple invasive species can be complex because ecological relationships, which occur among several trophic levels, are often incompletely understood. Further, the complexity of these trophic relationships exacerbates our inability to predict climate change effects on invaded ecosystems. We explore the hypothesis that interactions between two global change drivers, invasive vertebrates and climate change, will potentially make matters worse for native biodiversity. In New Zealand beech (Nothofagus spp.) forests, a highly irruptive invasive mammal community is driven by multi-annual resource pulses of beech seed (masting). Because mast frequency is predicted to increase with climate change, we use this as a model system to explore the extent to which such effects may influence invasive vertebrate communities, and the implications of such interactions for native biodiversity and its management. We build on an established model of trophic interactions in the system, combining it with a logistic probability mast function, the parameters of which were altered to simulate either contemporary conditions or conditions of more or less frequent masting. The model predicts that increased mast frequency will lead to populations of a top predator (the stoat) and a mesopredator (the ship rat) becoming less irruptive and being maintained at appreciably higher average abundances in this forest type. In addition, the ability of both current and in-development management approaches to suppress invasive mammals is predicted to be compromised. Because invasive mammals are key drivers of native fauna extinction in New Zealand, with the additional loss of associated functions such as pollination and seed dispersal, these predictions imply potentially serious adverse impacts of climate change for the conservation of biodiversity and ecosystem function. Our study also highlights the importance of long-term monitoring data for assessing and managing future impacts of global change drivers.