Interannual variability in the global land carbon sink is strongly related to variations in tropical temperature and rainfall. This association suggests an important role for moisture-driven fluctuations in tropical vegetation productivity, but empirical evidence to quantify the responsible ecological processes is missing. Such evidence can be obtained from tree-ring data that quantify variability in a major vegetation productivity component: woody biomass growth. Here we compile a pantropical tree-ring network to show that annual woody biomass growth increases primarily with dry-season precipitation and decreases with dry-season maximum temperature. The strength of these dry-season climate responses varies among sites, as reflected in four robust and distinct climate response groups of tropical tree growth derived from clustering. Using cluster and regression analyses, we find that dry-season climate responses are amplified in regions that are drier, hotter and more climatically variable. These amplification patterns suggest that projected global warming will probably aggravate drought-induced declines in annual tropical vegetation productivity. Our study reveals a previously underappreciated role of dry-season climate variability in driving the dynamics of tropical vegetation productivity and consequently in influencing the land carbon sink.