Earthen dams, as critical infrastructures in water resources management, play a key role in water supply, hydroelectric power generation, and flood control. However, uncontrolled seepage threatens the stability of these structures by increasing pore water pressure and inducing internal erosion. This study investigated the effect of a 10% increase in drain dimensions, including length and thickness, on the hydraulic performance and stability of Sahand earthen dam in East Azerbaijan Province, Iran, using finite element numerical modeling in SEEP/W software. The field data were validated with a 95.5% agreement and an error of less than 4.5%, and Laplace’s equation was employed for steady-state flow analysis. A Monte Carlo sensitivity analysis with 1,000 scenarios, along with machine learning algorithms, was applied to optimize the drain dimensions. The quantitative results showed that the seepage discharge increased by 25%, from 0.012 to 0.015 m³/s, while pore water pressure decreased by 12.8%, hydraulic head decreased by 4%, and the hydraulic gradient remained within the safe range in up to 95% of the analyzed conditions. From a qualitative perspective, slope stability improved by up to 90%, the risk of internal erosion decreased by up to 92%, and better seepage control was achieved under steady-state conditions. Based on field validation, these findings are generalizable to similar dams with an accuracy of 98% and provide a practical approach for enhancing dam safety under climate change conditions. Nevertheless, transient flow analysis under variable climatic conditions is suggested for future studies.