<p>As generative AI (GenAI) becomes increasingly embedded in higher education, understanding how students engage with this technology is critical. Using an Extended Unified Theory of Acceptance and Use of Technology (UTAUT) framework, this study explores the role of AI literacy in shaping student engagement among doctoral students with prior awareness or usage experience of GenAI. Specifically, we examine how AI literacy influences performance and effort expectancy, which in turn affect three dimensions of student engagement: behavioral (e.g., time and effort invested in learning), affective (e.g., interest in learning and sense of belonging), and cognitive (e.g., deep thinking and cognitive strategies). Data from 626 Chinese doctoral students reveal that AI literacy significantly enhances performance and effort expectancy, fostering behavioral and affective engagement, though not cognitive engagement. Furthermore, social influence and facilitating conditions strengthen the link between AI literacy and cognitive appraisals. Mediation analysis shows performance expectancy primarily drives affective engagement, while effort expectancy mediates behavioral engagement. Notably, the findings also uncover meaningful differences across gender, university types, and disciplinary backgrounds, highlighting the importance of context-specific strategies for GenAI integration in doctoral education.</p>