Invasive species continue to severely impact biodiversity, yet predicting the success or failure of introduced species has remained elusive. In particular, the relationship between community invasibility and native species diversity remains obscure. Here, we apply two traditional ecological concepts that inform prey population stability and hence invasibility. We first show that the native predatory crustacean Gammarus duebeni celticus exhibited similar type II (destabilizing) functional responses (FRs) towards native mayfly prey and invasive amphipod prey, when these prey species were presented separately. However, when the two prey species were presented simultaneously, the predator did not exhibit prey switching, instead consuming disproportionately more native prey than expected from the relative abundance of native and invasive species. These consumptive propensities foster reductions of native prey, while simultaneously limiting biotic resistance against the invasive species by the native predator. Since our theoretical considerations and laboratory results match known field invasion patterns, we advocate the increased consideration of FR and prey switching studies to understand and predict the success of invasive species.