The literature on generative "Artificial Intelligence" (AI) in education primarily focuses on its immediate benefits and applications, such as personalized learning, student engagement, and content generation. However, there is a notable absence of empirical research concerning the holistic use of generative AI within educational institutions and its long-term impact on educational sustainability. This study investigates the factors that predict the use of generative AI and its subsequent influence on educational sustainability. This study enhanced the extended "Unified Theory of Acceptance and Use of Technology" (UTAUT-2) by including personal innovativeness as an external variable and educational sustainability as an outcome. A hybrid methodology, integrating "Structural Equation Modeling" (SEM) and "Artificial Neural Network" (ANN), was used to evaluate the research model using data collected from 1,011 university students. The SEM analysis confirmed all hypotheses. Specifically, a positive relationship was found between use behavior and educational sustainability. These results show that the combined variables collectively account for 63% and 66% of the variance in use behavior and educational sustainability, respectively. The sensitivity analysis identified habit as the most important predictor of use behavior. The findings offer both theoretically important and practically valuable implications for designing user-centered AI integration in education.