Global hydrological models (GHMs) supply key information for stakeholders and policymakers simulating past, present and future water cycles. Inaccuracy in GHM simulations, i.e., simulation results that poorly match observations, leads to uncertainty that hinders valuable decision support. Improved parameter estimation is one key to more accurate simulations of global models. Here, we introduce an efficient and transparent way to understand the parameter control of GHMs to advance parameter estimation using global sensitivity analysis (GSA). In our analysis, we use the GHM WaterGAP3 and find that the most influential parameters in 50% of 347 basins worldwide are model parameters that have traditionally not been included when calibrating this model. Parameter importance varies in space and between metrics. For example, a parameter that controls groundwater flow velocity is influential on signatures related to the flow duration curve but not on traditional statistical metrics. Parameters linked to evapotranspiration and high flows exhibit unexpected behaviour, i.e., a parameter defining potential evapotranspiration influences high flows more than other parameters we would have expected to be relevant. This unexpected behaviour suggests that the model structure could be improved. We also find that basin attributes explain the spatial variability of parameter importance better than Köppen-Geiger climate zones. Overall, our results demonstrate that GSA can effectively inform parameter estimation in GHMs and guide the improvement of the model structure. Thus, using GSA to advance parameter estimation supports more accurate simulations of the global water cycle and more robust information for stakeholders and policymakers.