The intensification of the hydrological cycle, with an observed and modeled increase in drought incidence and severity, underscores the need to quantify drought effects on carbon cycling and the terrestrial sink. FLUXNET, a global network of eddy covariance towers, provides dense data streams of meteorological data, and through flux partitioning and gap filling algorithms, estimates of net ecosystem productivity (FNEP), gross ecosystem productivity (P), and ecosystem respiration (R). We analyzed the functional relationship of these three carbon fluxes relative to evaporative fraction (EF), an index of drought and site water status, using monthly data records from 238 micrometeorological tower sites distributed globally across 11 biomes. The analysis was based on relative anomalies of both EF and carbon fluxes and focused on drought episodes by biome and climatic season. Globally P was ≈50% more sensitive to a drought event than R. Network-wide drought-induced decreases in carbon flux averaged −16.6 and −9.3 g C m−2 month−1 for P and R, i.e., drought events induced a net decline in the terrestrial sink. However, in evergreen forests and wetlands drought was coincident with an increase in P or R during parts of the growing season. The most robust relationships between carbon flux and EF occurred during climatic spring for FNEP and in climatic summer for P and R. Upscaling flux sensitivities to a global map showed that spatial patterns for all three carbon fluxes were linked to the distribution of croplands. Agricultural areas exhibited the highest sensitivity whereas the tropical region had minimal sensitivity to drought. Combining gridded flux sensitivities with their uncertainties and the spatial grid of FLUXNET revealed that a more robust quantification of carbon flux response to drought requires additional towers in all biomes of Africa and Asia as well as in the cropland, shrubland, savannah, and wetland biomes globally.