The migration and fate of pesticides in natural environments is highly complex. At the hillslope scale, the quantification of contaminant fluxes and concentrations requires a physically based model. This class of model has recently been extended to include coupling between the surface and the subsurface domains for both the water flow and solute transport regimes. Due to their novelty, the relative importance of and interactions between the main model parameters has not yet been fully investigated. In this study, a global Sobol sensitivity analysis is performed on a vineyard hillslope for a one hour intensive rain event with the CATHY (CATchment HYdrology) integrated surface/subsurface model. The event-based simulation involves runoff generation, infiltration, surface and subsurface solute transfers, and shallow groundwater flow. The results highlight the importance of the saturated hydraulic conductivity Ks and the retention curve shape parameter n and they reveal a strong role for parameter interactions associated with the exchange processes represented in the model. The mass conservation errors generated by the model are lower than 1% in 99.7% of the simulations. Boostrapping analysis of sampling methods and errors associated with the Sobol indices highlights the relevance of choosing a large sampling size (at least N = 1000) and raises issues associated with rare but extreme output results.