The simulation of non-point source pollution in agricultural basins is a computationally demanding process due to the large number of individual sources and potential pollution receptors (e.g., drinking water wells). In this study, we present an efficient computational framework for parallel simulation of diffuse pollution in such groundwater basins. To derive a highly detailed velocity field, we employed algebraic multigrid (AMG) preconditioners to solve the groundwater flow equation. We compare two variants of AMG implementations, the multilevel preconditioning provided by Trilinos and the BoomerAMG provided by HYPRE. We also perform a sensitivity analysis on the configuration of AMG methods to evaluate the application of these libraries to groundwater flow problems. For the transport simulation of diffuse contamination, we use the streamline approach, which decomposes the 3D transport problem into a large number of 1D problems that can be executed in parallel. The proposed framework is applied to a 2,600-km2 groundwater basin in California discretized into a grid with over 11 million degrees of freedom. Using a Monte Carlo approach with 200 nitrate loading realizations at the aquifer surface, we perform a stochastic analysis to quantify nitrate breakthrough prediction uncertainty at over 1,500 wells due to random, temporally distributed nitrate loading. The results show that there is a significant time lag between loading and aquifer response at production wells. Generally, typical production wells respond after 5–50 years depending on well depth and screen length, while the prediction uncertainty for nitrate in individual wells is very large—approximately twice the drinking water limit for nitrate.