Understanding the characteristics and correlations between evapotranspiration and climate variables plays a crucial role in determining the probable impact of critical factors on crop water requirements, water resource management, and future planning. This work aims to evaluate the temporal trends of evapotranspiration and its sensitivity to climate variables from 1980 to 2019 in Southeast, Vietnam. The improved Innovative Şen Trend Analysis method was used to identify trends, and the Sobol technique, based on variance-based analysis, allowed for a rapid calculation of sensitivity indices. By estimating the changes in evapotranspiration, the study confirmed different quantitative trends, including a significant increase of 72–135 mm in annual and 12–84 mm in seasonal evapotranspiration. Results also conducted a sensitivity analysis of the historical meteorological quantiles obtained for three climate stations to analyze the sensitivity indices. The sensitivity analysis showed that evapotranspiration is more sensitive to solar radiation, relative humidity, and minimum temperature. The study presents pragmatic approaches for considering the possible interactions between evapotranspiration and climate variables, which may serve as a baseline for sustainable water management in areas with similar climate conditions and adaptation to climate change.