Higher levels of taxonomic and evolutionary diversity are expected to maximize ecosystem function, yet their relative importance in driving variation in ecosystem function at large scales in diverse forests is unknown. Using 90 inventory plots across intact, lowland, terra firme, Amazonian forests and a new phylogeny including 526 angiosperm genera, we investigated the association between taxonomic and evolutionary metrics of diversity and two key measures of ecosystem function: aboveground wood productivity and biomass storage. While taxonomic and phylogenetic diversity were not important predictors of variation in biomass, both emerged as independent predictors of wood productivity. Amazon forests that contain greater evolutionary diversity and a higher proportion of rare species have higher productivity. While climatic and edaphic variables are together the strongest predictors of productivity, our results show that the evolutionary diversity of tree species in diverse forest stands also influences productivity. As our models accounted for wood density and tree size, they also suggest that additional, unstudied, evolutionarily correlated traits have significant effects on ecosystem function in tropical forests. Overall, our pan-Amazonian analysis shows that greater phylogenetic diversity translates into higher levels of ecosystem function: tropical forest communities with more distantly related taxa have greater wood productivity.