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Global increase in drought occurrences threatens the stability of terrestrial ecosystem functioning. Evergreen broadleaf forests (EBFs) keep leaves throughout the year, and therefore could experience higher drought risks than other biomes. However, the recent temporal variability of global vegetation productivity or land carbon sink is mainly driven by non-evergreen ecosystems, such as semiarid grasslands, croplands, and boreal forests. Thus, we hypothesize that EBFs have higher stability than other biomes under the increasingly extreme droughts. Here we use long-term Standardized Precipitation and Evaporation Index (SPEI) data and satellite-derived Enhanced Vegetation Index (EVI) products to quantify the temporal stability (ratio of mean annual EVI to its SD), resistance (ability to maintain its original levels during droughts), and resilience (rate of EVI recovering to pre-drought levels) at biome and global scales. We identified significantly increasing trends of annual drought severity (SPEI range: -0.08 to -1.80), area (areal fraction range: 2%-19%), and duration (month range: 7.9-9.1) in the EBF biome over 2000-2014. However, EBFs showed the highest resistance of EVI to droughts, but no significant differences in resilience of EVI to droughts were found among biomes (forests, grasslands, savannas, and shrublands). Global resistance and resilience of EVI to droughts were largely affected by temperature and solar radiation. These findings suggest that EBFs have higher stability than other biomes despite the greater drought exposure. Thus, the conservation of EBFs is critical for stabilizing global vegetation productivity and land carbon sink under more-intense climate extremes in the future.