As global warming produces dramatic climate changes, water management is facing increasingly serious challenges. Given to the process of climate change and its complex effects on watershed hydrology, this paper investigates the spatial and temporal variation characteristics of major climatic factors (i.e., precipitation and temperature) over the upper Yangtze River basin (UYRB), China. The statistical analyses are based on annual and seasonal scales during 1951–2020 with a recorded period of seven decades. The Mann–Kendall nonparametric test and R/S analysis are used to record the temporal trends (past and future) of climate variables; the Pettitt test, standard normal homogeneity test and Buishand test are used to detect the homogeneity in climate series. The sensitivities of the streamflow to climatic parameters are assessed at the watershed scale, especially considering the Three Gorges Dam’s (TGD) effect on changing runoff. The results of the study indicate that the annual precipitation of 29 out of 34 series indicate homogeneity, while 31 out of 34 annual mean temperature series show heterogeneity, with jump points around 1997 in the mean temperature of 20 sites. Detectable changes in precipitation were not observed during 1951–2020; however, the temperature increased significantly in the whole basin on annual and seasonal scales, except for several stations in the eastern part. The magnitude of increase in air temperature in high altitudes (Tibet Plateau) is higher than that in low altitudes (Sichuan Plain) over the last seven decades, and future temperatures continue to sharply increase in high altitudes. The TGD plays an important role in explaining the seasonal variations in streamflow at Yichang station, with streamflow experiencing a sharp increase in winter and spring (dry season) and a decrease in summer and autumn (rainy season) compared to the pre-TGD period. The streamflow variation at an annual scale is mainly regulated by climate fluctuation (variation in precipitation). During the last seven decades, increasing air temperature and decreases in rainfall and runoff signify reduced water resources availability, and the climate tends to be warmer and drier over the basin. The sensitivity of the streamflow to watershed precipitation is higher than that to temperature, with variation in annual rainfall explaining 71% of annual runoff variability.