Basin-scale water scarcity, an adverse consequence of the imbalance between the available fresh water and water demands, is an alarming situation in many countries worldwide. This necessitates for analyzing the risk of water scarcity forced with the changing climate, land-use alterations, growing population, and industrialization to pave a way for sustainable water resources systems planning and management. This study advocates a hydrological model-based evaluation approach employing Soil Water Assessment Tool (SWAT) to identify the dominating drivers on the decadal streamflow patterns and other basin-scale water balance components, viz., blue water flow (BWF), green water storage (GWS), and green water flow (GWF) in the Brahmani and Baitarani River basins of eastern India. The results reveal that, in these basins, the climate change effect has relatively a higher impact on streamflow than the land-use change. This study surmises that the Brahmani and Baitarani River basins can be categorized under the high- and moderate-risk water scarcity zones, respectively. The developed approach of assessing the water scarcity risk under the non-availability of basin-scale sectoral water demands could be a reliable tool for many data-scarce river basins worldwide.