Unveiling the mechanisms that promote coexistence in biological communities is a fundamental problem in ecology. Stable coexistence of many species is commonly observed in natural communities. Most of these natural communities, however, are composed of species from multiple trophic and functional groups, while theory and experiments on coexistence have been focusing on functionally similar species. Here, we investigated how functional diversity affects the stability of species coexistence and productivity in multispecies communities by characterizing experimentally all pairwise species interactions in a pool of 11 species of eukaryotes (10 protists and one rotifer) belonging to three different functional groups. Species within the same functional group showed stronger competitive interactions compared to among-functional group interactions. This often led to competitive exclusion between species that had higher functional relatedness, but only at low levels of species richness. Communities with higher functional diversity resulted in increased species coexistence and community biomass production. Our experimental findings and the results of a stochastic model tailored to the experimental interaction matrix suggest the emergence of strong stabilizing forces when species from different functional groups interact in a homogeneous environment. By combining theoretical analysis with experiments we could also disentangle the relationship between species richness and functional diversity, showing that functional diversity per se is a crucial driver of productivity and stability in multispecies community.