Biological invasions by large herbivores involve the establishment of novel interactions with the receiving mammalian carnivore community, but understanding these interactions is difficult due to the large spatiotemporal scales at which such dynamics would occur. We quantified the functional responses of a native apex predator (the dingo (Canis familiaris), which includes wild dogs and their hybrids) and a non-native mesopredator (red fox; Vulpes vulpes) to an invading non-native ungulate (sambar deer; Cervus unicolor) in Australia. We predicted that the apex predator would exhibit a stronger functional response to increasing sambar deer abundance than the mesopredator. We used a state–space model to link two 30-year time series: (i) sambar deer abundance (hunter catch-per-unit-effort); and (ii) percentages of sambar deer in dingo (N = 4531) and fox (N = 5002) scats. Sambar deer abundance increased over fourfold during 1984–2013. The percentages of sambar deer in dingo and fox scats increased during this 30-year period, from nil in both species in 1984 to 8.2% in dingoes and 0.5% in foxes in 2013. Dingoes exhibited a much stronger functional response to increasing sambar deer abundance than foxes. The prediction that invading deer would be utilized more by the apex predator than by the mesopredator was therefore supported. The increasing abundance of sambar deer during the period 1984–2013 provided an increasingly important food source for dingoes. In contrast, the smaller red fox utilized sambar deer much less. Our study demonstrates that prey enrichment can be an important consequence of large herbivore invasions and that the effect varies predictably with the trophic position of the mammalian carnivores in the receiving community.