The widespread adoption of generative artificial intelligence tools among university students has introduced pressing questions about the cognitive consequences of AI dependence, particularly with respect to critical thinking a higher-order competency essential to academic achievement and lifelong intellectual development. This quantitative, survey-based study investigates the influence of generative AI dependence on students' critical thinking skills and examines the moderating role of academic self-regulation in this relationship. A stratified sample of 200 undergraduate and postgraduate students was selected using stratified random sampling from four public universities across a province in Pakistan. Data were collected using three validated instruments: the Generative AI Dependence Scale (GAIDS), the Critical Thinking Skills Scale (CTSS), and the Academic Self-Regulation Scale (ASRS). Descriptive statistical analysis revealed that a substantial proportion of students exhibit moderate-to-high generative AI dependence, which is descriptively associated with lower critical thinking skill levels across five measured dimensions: analysis, interpretation, inference, evaluation, and explanation. Crucially, students with high academic self-regulation consistently report stronger critical thinking skills regardless of their AI dependence level, suggesting that self-regulation functions as a meaningful cognitive buffer against the critical thinking impairment associated with excessive AI reliance. These findings contribute original, context-specific empirical evidence to an emerging and rapidly growing field and offer targeted recommendations for curriculum design and institutional AI governance.