A coupled groundwater-flow-modelling and vulnerability-mapping methodology for the management of karst aquifers with spatial variability is developed. The methodology takes into consideration the duality of flow and recharge in karst and introduces a simple method to integrate the effect of temporal storage in the unsaturated zone. In order to investigate the applicability of the developed methodology, simulation results are validated against available field measurement data. The criteria maps from the PaPRIKa vulnerability-mapping method are used to document the groundwater flow model. The FEFLOW model is employed for the simulation of the saturated zone of Palaikastro-Chochlakies karst aquifer, in the island of Crete, Greece, for the hydrological years 2010–2012. The simulated water table reproduces typical karst characteristics, such as steep slopes and preferred drain axes, and is in good agreement with field observations. Selected calculated error indicators—Nash-Sutcliffe efficiency (NSE), root mean squared error (RMSE) and model efficiency (E′)—are within acceptable value ranges. Results indicate that different storage processes take place in different parts of the aquifer. The north-central part seems to be more sensitive to diffuse recharge, while the southern part is affected primarily by precipitation events. Sensitivity analysis is performed on the parameters of hydraulic conductivity and specific yield. The methodology is used to estimate the feasibility of artificial aquifer recharge (AAR) at the study area. Based on the developed methodology, guidelines were provided for the selection of the appropriate AAR scenario that has positive impact on the water table.