A variably-saturated finite element model HYDRUS-2D was used to simulate the spatiotemporal dynamics of stream-aquifer exchange for a perennial stream flowing through an undulating catchment and underlain by heterogeneous geology. The model was first calibrated and validated using piezometric heads measured near the stream. The model was then used a) to quantify the long-term dynamics of exchange at stream-aquifer interface and the water balance in the domain, and b) to evaluate the impact of anisotropy of geological materials, thickness (w) and hydraulic conductivity (Ks) of the low permeability layer at the streambed, and water table fluctuations on the extent of exchange. Simulated pressure heads in the domain revealed that seasonal groundwater fluctuations were more pronounced near the stream. Daily discharge to the stream varied from 0.05 to 0.3 mm/day, annual discharge ranged from 59 to 74 mm, and the overall water balance showed a discharge (−54 mm) from the domain during 2000–2012. A five-fold increase in Ks of the low permeability layer enhanced discharge to the stream by 14% (10 mm/year) whereas an increase in the thickness of the layer by 1 m had a low impact (2.4 mm/year). A 2-m drawdown of the water table transformed a connected and gaining system into a losing, disconnected system. These results suggest that depletion of groundwater due to climate change or excessive pumping could have a pronounced impact on the availability of water resources and sustainability of the existing water-dependent ecosystem.