Mountain watersheds, serving as critical regional water sources, were highly sensitive to climate change. Investigating hydrological changes in mountain watersheds provided vital theoretical support for the protection of regional ecological environments and the sustainable use of water resources under changing conditions. This study focused on the Qinling Mountain Area and its six typical watersheds. Utilizing daily meteorological data from 79 meteorological stations from 1965 to 2019, annual runoff data from hydrological control stations within the watersheds, annual sunspot numbers, atmospheric circulation indices, and the Nino3.4 index, techniques such as the Penman-Monteith equation, a Modified Mann-Kendall trend test, differential methods, cross wavelet transforms, and the time-varying Budyko framework were employed to analyze the spatiotemporal variations in potential evapotranspiration (PET) across the Qinling Mountain Area, assess PET sensitivity to various climatic factors, explore the potential drivers of PET changes, and finally, quantify the contributions of PET and other factors to runoff variations across different periods. The results indicated: 1) significant differences of spatial distribution and trends in multi-year average PET and climate factors from 1965 to 2019. Multi-year average PET and sunlight hours (SH) exhibited a spatial pattern of being higher in the northeast and lower in the southwest, while the maximum and minimum relative humidity (RHmax and RHmin) showed opposite trends. Additionally, on an annual scale, temperature generally increased, while SH and wind speed (WS) decreased across a broad area. The average annual WS of all vegetation types did not exceed 1.8 m/s, and the areas with significant reduction in annual WS were mainly concentrated in vegetation types such as broad-leaved forest, cultivated vegetation, shrub, coniferous forest, and grass (p <0.05). Research found that differential methods could accurately simulate the annual variation of PET in the Qinling Mountain Area on an annual scale, with the coefficient of certainty R2 between the calculated value and the actual value reaching 0.96. 2) The annual PET and climatic factors exhibited different patterns of change across various vegetation types, such as a significant decrease in SH in broadleaf forests and cultivated vegetation areas, with spatially uneven distribution of relative humidity change trends (p <0.05). The sensitivity of annual PET to annual SH showed an overall pattern of low in the north and high in the east and west in spatial distribution, with a value range of -0.04~0.04. However, the sensitivity of PET to RHmax did not show a clear spatial distribution pattern. The sensitivity of annual PET to multiple climatic factors was highest in grassland vegetation areas. The influence of topographical factors, solar activity, and atmospheric circulation on annual PET varied in duration and scope. PET showed a highly significant decreasing trend with increasing elevation and slope (p <0.001), with 98.73% of meteorological stations showing a negative correlation between annual PET and the Arctic Oscillation index (AO index), and 20.25% showing a significant negative correlation (p <0.05). 3) Among the six typical watersheds, the three northern foothill watersheds showed a decreasing trend in annual runoff depth, while two of the three southern foothill watersheds exhibited an increasing trend. In different typical watersheds and sliding window periods, the impact of PET on runoff changes in the Qinling Mountain Area was generally relatively small. Changes in vegetation and other surface conditions were the primary factors driving watershed runoff changes, increasingly impacting watershed runoff, warranting future focus. This research underpinned the sustainable utilization of water resources in mountain watersheds, supporting ecological protection and high-quality development in the Yellow River and Yangtze River Basins. This study highlighted the importance of continuous monitoring and adaptive management strategies in response to ongoing and future climatic changes. The integration of multiple types of data and reliable hydrological analysis methods provided a comprehensive understanding of the complex interactions between climatic factors and hydrological processes in mountainous regions.