Abstract Droughts are projected to increase in magnitude, frequency and duration in the near future. In rangelands, the provision of valuable ecosystem services such as forage supply for livestock productivity is intimately linked to rainfall patterns, which makes it particularly vulnerable to droughts. Nonetheless, rangelands can differ in their sensitivity to droughts as shown by strong differences in the impacts of inter‐annual precipitation changes on vegetation productivity in different sites. The aim of this study was to assess the sensitivity to droughts of nine rangelands located across a broad aridity gradient in Argentina, South America. We experimentally imposed comparable droughts under field conditions by reducing a fixed proportion of each incoming precipitation event within‐year during three consecutive years and tracked changes in total aboveground and forage productivity. We found that arid and semi‐arid rangelands were more severely impaired in their forage provision by drought than mesic rangelands, that is that sensitivity to drought declined as aridity decreased. Forage productivity decreased on average by c. 50%, in arid and semi‐arid rangelands, whereas mesic sites did not exhibit significant changes between drought and control treatments. The negative impact in forage productivity of arid and semi‐arid rangelands was mainly driven by the productivity reduction of few key plant species at each site. In seven of the nine rangelands, we found detrimental effects of drought on forage productivity during the first experimental‐drought year, and in five of them the impact was further accentuated until the end of the experiment, which indicates how serious can these events be. Synthesis and applications. Our main findings indicate that the drought‐induced impacts on forage provision are higher as aridity increases. This pattern highlights the urgent need to implement strategies to mitigate the detrimental consequences of drought, particularly in arid and semiarid rangelands, where forage provision is strongly associated with human well‐being. Management approaches focused on key forage species, such as reducing the grazing pressure during drought periods according to these species' productivity dynamics can attenuate impacts on vulnerable ecosystems, preserving the rangelands' integrity while maintaining high long‐term productivity levels.