Although prior studies have established the educational potential of artificial intelligence tools, limited empirical attention has been given to how cognitive capabilities shape the relationship between generative AI use and students’ problem-solving efficacy, particularly within African higher education. Based on the integration model between the Technology Acceptance Model (TAM) and Social Cognitive Theory (SCT), this study explores the impact of ChatGPT usage on mathematical problem-solving efficacy among university students, with digital literacy and critical thinking as mediators. A cross-sectional study was designed, and the sample consisted of 375 undergraduate students from universities across Ghana. A validated measurement approach was used with a focus on establishing and ensuring reliability and construct validity. In addition, a model test was done using structural equation modeling with a software package called AMOS version 23. Results suggest a positive and significant impact of ChatGPT usage on students’ mathematical problem-solving efficacy. Moreover, partial mediation was observed for digital literacy and critical thinking. This implies that improved AI-based learning tools are dependent not only on their usage but also on students’ cognitive performance. These findings imply that universities should adopt AI tools and pedagogic interventions that promote critical thinking and digital literacy among students. Originality/value: This study advances theory by empirically integrating TAM and SCT to explain AI-supported problem-solving in an under-researched African higher education context, offering nuanced insights into the cognitive pathways through which generative AI enhances learning effectiveness.