Generalist predator populations often surge during resource pulses but decline sharply afterwards and shift to alternative prey sources, which experience elevated predation rates. Understanding these numerical and functional responses of predators to resource pulses is especially important for effectively managing island ecosystems, where invasive mammals are generalist predators and vulnerable indigenous birds are alternative prey. We used DNA metabarcoding of stomach contents to test whether the proportion of black rats (Rattus rattus) consuming birds changed during and after a mast seeding year in a New Zealand beech forest. Contrary to prevailing assumptions that black rats in forests consume birds only occasionally and increase their consumption of birds once a resource pulse finishes, we found that the overall proportion of rats consuming birds was surprisingly high (19.4%), and that the proportion of rats consuming birds did not change significantly across the three years of a beech mast cycle. We detected 15 unique bird taxa in the rat stomachs and 40 unique plant taxa. The frequency of beech consumption declined across the three years, as predicted. We conclude that (1) forest birds are a common part of rat diet rather than an occasional opportunistic prey item, and (2) the impact of black rats on indigenous birds following seed pulses is predominantly driven by the numerical response (increased numbers of rats present) rather than a functional (prey switching) response. Conservation interventions that seek to maximally and consistently suppress rats are therefore likely to have the best outcomes for birds.