Trends in streamflow, rainfall and potential evapotranspiration (PET) time series, from 1970 to 2017, were assessed for five important hydrological basins in Southeastern Brazil. The concept of elasticity was also used to assess the streamflow sensitivity to changes in climate variables, for annual data and 5-, 10- and 20-year moving averages. Significant negative trends in streamflow and rainfall and significant increasing trend in PET were detected. For annual analysis, elasticity revealed that 1% decrease in rainfall resulted in 1.21–2.19% decrease in streamflow, while 1% increase in PET induced different reductions percentages in streamflow, ranging from 2.45% to 9.67%. When both PET and rainfall were computed to calculate the elasticity, results were positive for some basins. Elasticity analysis considering 20-year moving averages revealed that impacts on the streamflow were cumulative: 1% decrease in rainfall resulted in 1.83–4.75% decrease in streamflow, while 1% increase in PET induced 3.47–28.3% decrease in streamflow. This different temporal response may be associated with the hydrological memory of the basins. Streamflow appears to be more sensitive in less rainy basins. This study provides useful information to support strategic government decisions, especially when the security of water resources and drought mitigation are considered in face of climate change.