Complementary resource use and redundancy of species that fulfill the same ecological role are two mechanisms that can respectively increase and stabilize process rates in ecosystems. For example, predator complementarity and redundancy can determine prey consumption rates and their stability, yet few studies take into account the multiple predator species attacking multiple prey at different rates in natural communities. Thus, it remains unclear whether these biodiversity mechanisms are important determinants of consumption in entire predator-prey assemblages, such that food-web interaction structure determines community-wide consumption and stability. Here, we use empirical quantitative food webs to study the community-wide effects of functional complementarity and redundancy of consumers (parasitoids) on herbivore control in temperate forests. We find that complementarity in host resource use by parasitoids was a strong predictor of absolute parasitism rates at the community level and that redundancy in host-use patterns stabilized community-wide parasitism rates in space, but not through time. These effects can potentially explain previous contradictory results from predator diversity research. Phylogenetic diversity (measured using taxonomic distance) did not explain functional complementarity or parasitism rates, so could not serve as a surrogate measure for functional complementarity. Our study shows that known mechanisms underpinning predator diversity effects on both functioning and stability can easily be extended to link food webs to ecosystem functioning.