Climate change significantly impacts the formation of water resources and the transformation of hydrological elements within basins. Accurately quantifying river runoff responses to climate change is crucial for the sustainable development and efficient utilization of water resources. However, research on hydrological climate elasticity under non-stationary conditions remains relatively limited. This study focuses on eight sub-basins in the mountainous region of the Baiyangdian Lake Basin, employing a newly developed non-stationary runoff elasticity coefficient analysis method based on the Budyko model to examine the annual runoff response to climate change. The proposed method is validated in a Chinese basin, broadening its applicability, and is compared with results obtained using the Budyko model-based elasticity method under multi-year stationary conditions. The results reveal the following: on an annual scale, the annual evapotranspiration ratio and water storage change ratio exhibit a strong linear correlation with the annual aridity index; runoff is more sensitive to changes in precipitation at both annual and multi-year time scales; the annual runoff elasticity coefficient is smaller than the coefficient calculated under multi-year stationary conditions, highlighting the significant regulatory role of basin water storage in runoff responses to climate change. Furthermore, the annual elasticity coefficient is strongly correlated with basin area. This study validates the effectiveness of the newly proposed non-stationary runoff elasticity coefficient method based on the Budyko model and extends its applicability from humid regions to semi-humid and semi-arid areas. These findings provide valuable guidance for the sustainable management of water resources in the Baiyangdian Lake Basin and the Xiong’an New Area.