Background <p>Increasing digital engagement among university faculty has intensified screen exposure, extended working hours, and disrupted sleep, potentially contributing to burnout. This study investigated the relationships between digital engagement and burnout among university faculty in India, with a particular focus on the mediating roles of weekly work hours and sleep patterns.</p> Methods <p>A national cross-sectional online survey was conducted among 3,987 university faculty members across all geographical regions of India between February and October 2024. Data included socio-demographic characteristics, daily screen time, sleep quality assessed using the Pittsburgh Sleep Quality Index, physical activity levels, and burnout measured using the Copenhagen Burnout Inventory. Multiple regression analyses were performed to identify predictors of personal, work-related, and client-related burnout. Mediation analyses examined indirect effects of work hours and sleep duration on the relationship between screen time and burnout outcomes.</p> Results <p>Participants (mean age: 43.92 years; mean professional experience: 15.77 years) reported significant screen exposure (5.02&#xa0;h daily) and poor sleep quality (PSQI: 7.5). Multiple regression analyses (<i>N</i> = 3,987) suggest sleep hours, weekly work hours, and screen time as universal burnout predictors. Daily screen time was associated with burnout outcomes in adjusted analyses, with mediation models indicating that these relationships were primarily indirect. Higher screen time was associated with increased weekly work hours, which in turn were linked to higher burnout, while more sleep duration showed a protective association with reduced burnout. Screen time also demonstrated a direct effect on personal burnout (<i>β = 0.327</i>, <i>p</i> &lt; .001), alongside indirect effects via work hours (<i>β = 0.301</i>, <i>p</i> &lt; .001) and sleep duration (<i>β = -0.109</i>, <i>p</i> &lt; .001). Notably, the direct effect was observed only for personal burnout, whereas the associations with work-related and client-related burnout were predominantly mediated.</p> Conclusion <p>The findings of this study highlight the possibility of screen time effects on burnout, which operates primarily through work-related demands and sleep-related mechanisms, emphasizing the importance of workload management and suggesting a recovery process in mitigating burnout among faculty members of higher education institutions.</p> Trial registration <p>The study protocol was prospectively registered with the Clinical Trial Registry India; assigned identifier: CTRI/2024/02/063155, dated 26/02/2024.</p>