A study on the complex processes of hydrogeological transformation of recharge into discharge within a karst system is described. Given the absence of boreholes or points of direct observation, the applied methodology is based on study of the natural response of the main outlet of the karst aquifer, considered here as a black-box. Time series analysis and recession curve analysis are applied to daily time series of rainfall as input, and spring discharge as the output of the aquifer. Daily variations of temperature and electrical conductivity of spring water are considered as well. The present study, an integrated research endeavor, is the first quantitative approach toward understanding the hydrogeological functioning of a large and not-well-known karst aquifer and improving existing knowledge about its internal physical characteristics. The case study is the Degracias-Sicó karst aquifer, in Portugal’s central-western region, which is relatively unknown from the hydrogeological perspective. The response of the karst aquifer’s main spring shows an important component of quick flow after heavy rainfall events and then a very slow recession. This bimodal behavior is proof of the significant spatial complexity and heterogeneity of the karst aquifer, marked by the presence of a conduit-dominated flow throughout a connected conduit network system and the dominance of base flow that confirms the aquifer’s large storage capacity. The results also demonstrate a significant component of delayed flow.