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The Tibetan Plateau, known as the "Asian water tower,"is a hotspot for complex hydroclimatic changes. We reveal that the previously decreasing atmospheric evaporative demand (Eo) trend at the end of the 20th century has reversed over the last two decades. Although both wind stilling and solar dimming have persisted, their effects on Eo rates have been overshadowed by increasing air temperatures and decreasing relative humidity, leading to a net rise in Eo for 1980-2015. Using the empirical "top-down"Budyko approach, we estimate that across seven sub-catchments draining the Tibetan Plateau, a 10% increase in annual-averaged precipitation, assuming all other factors remain constant, would lead to a 15%-19% increase in streamflow. Conversely, a 10% increase in annual-averaged Eo would decrease streamflow by 5%-9%. Our findings provide a deeper understanding of the accelerating hydroclimatic changes and their impact on surface water resources in the Tibetan Plateau.