There is currently no general consensus on how the spatial variability of rainfall impacts and propagates through complex hydrogeological systems. Most studies to date have focused on the effects of rainfall spatial variability (RSV) on river discharge, while paying little attention to other important aspects of system response. Here, we study the impacts of RSV on several responses of a hydrological model of an overexploited system. To this end, we drive a spatially distributed hydrogeological model for the semiarid Upper Guadiana basin in central Spain with stochastic daily rainfall fields defined at three different spatial resolutions (fine → 2.5 km × 2.5 km, medium → 50 km × 50 km, large → lumped). This enables us to investigate how (i) RSV at different spatial resolutions, and (ii) rainfall uncertainty, are propagated through the hydrogeological model of the system. Our results demonstrate that RSV has a significant impact on the modeled response of the system, by specifically affecting groundwater recharge and runoff generation, and thereby propagating through to various other related hydrological responses (river discharge, river‐aquifer exchange, groundwater levels). These results call into question the validity of management decisions made using hydrological models calibrated or forced with spatially lumped rainfall.