An accurate grasp of the influence of precipitation and temperature changes on the variation in both the magnitude and temporal patterns of runoff is crucial to the prevention of floods and droughts. However, there is a general lack of understanding of the ways in which runoff sensitivities to precipitation and temperature changes are associated with the CMIP5 scenarios. This paper investigates the hydrological response to future climate change under CMIP5 RCP scenarios by using the VIC model and then quantitatively assesses runoff sensitivities to precipitation and temperature changes under different scenarios by using a set of simulations with the control variable method. The source region of the Yellow River (SRYR) is an ideal area to study this problem. The results demonstrated that the precipitation effect was the dominant element influencing runoff change (the degree of influence approaching 23%), followed by maximum temperature (approaching 12%). The weakest element was minimum temperature (approaching 3%), despite the fact that the increases in minimum temperature were higher than the increases in maximum temperature. The results also indicated that the degree of runoff sensitivity to precipitation and temperature changes was subject to changing external climatic conditions.