The penetration of artificial intelligence (AI) is dramatically transforming higher education, yet the effects of its pervasive adoption remain inconclusive. By automating routine tasks, AI enhances teachers' operational efficiency, enabling them to reallocate cognitive resources toward high-impact activities and thereby deepening their professional engagement. However, overreliance on AI may also erode autonomy, diminish critical competencies, and foster cognitive dependence, potentially contributing to a sense of disconnection from the intrinsic value of teaching. This study examines how university teachers’ collaboration with generative AI influences their work engagement. Based on self-determination theory, the study constructs a dual-pathway model in which teacher–AI collaboration increases work engagement via psychological availability but reduces it through work alienation, with digital competency moderating the process. Using three-wave data collected from 317 university teachers in China, results revealed that psychological availability mediates the positive effect of teacher–AI collaboration on work engagement, while work alienation mediates its negative effect. Importantly, digital competence serves as a crucial boundary condition, amplifying the positive effect via psychological availability while mitigating the negative effect through work alienation. This study extends the self-determination theory in human–AI collaboration settings by showing how basic psychological needs can be either supported or undermined, leading to opposite effects on work engagement. The findings offer actionable insights for managers to navigate digital transformation in higher education.