Preventing further biodiversity loss requires understanding which processes threaten biodiversity and the effectiveness of management actions in mitigating them. Threatening processes can interact in complex and unexpected ways, but different threats are often managed independently. Here, we develop a conceptual model to identify the conditions needed for management of a single threat to achieve a net conservation benefit in systems with multiple interacting threats, and demonstrate its relevance in a replicated case-study experiment. In Australia, introduced red foxes (Vulpes vulpes) and feral cats (Felis catus) may hunt vulnerable native mammals more effectively after fire, due to loss of understory vegetation. However, the efficacy of broad-scale control of introduced predators in improving native mammal resilience to fire has not been quantified. Using a natural before-after control-impact experiment with 14 prescribed fires, each >200 ha, we tested whether existing landscape-scale fox baiting programs influenced the immediate effects of prescribed fire on these two introduced predators and five medium-sized native mammals, including the threatened long-nosed potoroo (Potorous tridactylus) and southern brown bandicoot (Isoodon obesulus). Fox occupancy increased across both treatments post-fire, but baiting reduced the magnitude of increase. In contrast, mean feral cat occupancy remained constant in unbaited areas post-fire, but nearly doubled in fox-controlled areas. Existing landscape-scale fox control programs did not clearly improve the short-term resilience of native mammals to prescribed fire (at least under the current fire and fox management regimes in our study landscapes). In the presence of acute disturbances such as fire, threatened native mammals may require more intensive and integrated management of fire and introduced predators, such as targeted predator control around fire events or protection using natural or artificial refuges).