Surface depressions are one of the important impact factors of hydrologic processes and catchment responses. However, in many hydrologic models, the influence of depressions is often simulated in a lumped manner, which results in the insufficient characterization of the filling–spilling–merging–splitting dynamics of depressions and the threshold behavior of the overland flow. The objective of the research reported in this paper is to improve the simulation of depression-influenced hydrologic processes by capturing the threshold control of depressions. To achieve this objective, a Depression-oriented Soil and Water Assessment Tool (SWAT-D) is developed. Specifically, the intrinsic changing patterns of contributing area and depression storage are first determined and further incorporated into the SWAT to simulate the filling–spilling of depressions and depression-influenced overland flow dynamics. The SWAT-D was applied to a depression-dominated watershed in the Prairie Pothole Region to evaluate its performance and capability. The simulated and observed hydrographs at the watershed outlet showed good agreement, with only a 7% deviation between the simulated and observed volumes of discharges in 2004. The NSE values for the simulated monthly average discharges during calibration and validation periods were 0.78 and 0.71, respectively, indicating the ability of the SWAT-D in reproducing the depression-influenced catchment responses. In addition, the SWAT-D was compared with other depression-oriented modeling techniques (i.e., the lumped depression approach and probability distribution models), and the comparisons emphasized the improvement of the SWAT-D and the importance of the research reported in this paper.