Distributed hydrological models based on shallow water equations have gained popularity in recent years for the simulation of storm events, due to their robust and physically based routing of surface runoff through the whole catchment, including hill slopes and water streams. However, significant challenges arise in their calibration due to their relatively high computational cost and the extensive parameter space. This study presents a surrogate-assisted evolutionary algorithm (SA-EA) for the calibration of a distributed hydrological model based on 2D shallow water equations. A surrogate model is used to reduce the computational cost of the calibration process by creating a simulation of the solution space, while an evolutionary algorithm guides the search for suitable parameter sets within the simulated space. The proposed methodology is evaluated in four rainfall events located in the northwest of Spain: one synthetic storm and three real storms in the Mandeo River basin. The results show that the SA-EA accelerates convergence and obtains superior fit values when compared to a conventional global calibration technique, reducing the execution time by up to six times and achieving between 98% and 100% accuracy in identifying behavioral parameter sets after four generations of the SA-EA. The proposed methodology offers an efficient solution for the calibration of complex hydrological models, delivering improved computational efficiency and robust performance.