Performance assessment of surface-water distribution systems in irrigation networks, particularly under water-shortage conditions, is essential for identifying poorly performing water-right holders and determining priorities for managerial intervention. This study aims to apply a compact, objective, and non-subjective multi-criteria framework based on Entropy weighting and the TOPSIS method for scenario-based performance assessment and prioritization of 675 irrigation units in the Jarghuyeh–Mahyar irrigation network. In this framework, the performance of irrigation units was evaluated using five criteria: adequacy index, efficiency index, dependability index, vulnerability, and relative distance from the canal head. The analyses were conducted under eight operational scenarios, including normal conditions, very low, low, medium, high, very high, exceptional, and unprecedented water-shortage conditions. After constructing the decision matrix and aligning the criteria directions, criterion weights were calculated for each scenario using the Entropy method. The irrigation units were then ranked using TOPSIS based on the closeness coefficient to the ideal solution. The results showed that, with increasing water shortage, the weight of the adequacy index increased from 0.071 under normal conditions to 0.687 under unprecedented water-shortage conditions. Moreover, the mean TOPSIS closeness coefficient decreased from 0.551 to 0.117, and the number of irrigation units classified as very poor increased from zero to 618. These findings indicate that the Entropy–TOPSIS framework can integrate performance and spatial criteria to rank and classify irrigation units under different water-shortage scenarios. Therefore, it can be used as a practical tool for identifying poorly performing water-right holders, prioritizing field inspections, and supporting improvements in surface-water distribution planning in irrigation networks.