Background: Prolonged use of smartphones, laptops, tablets and other digital devices is common among students. Sleep disturbance and changes in cognitive performance may occur in the context of prolonged screen exposure. Aim: To assess the prevalence of sleep disturbance and grades of neurocognitive dysfunction associated with prolonged digital screen exposure among students aged 18–25 years. Methods: A cross-sectional study was conducted among 122 students in Jalgaon district. Participants were assessed using the Pittsburgh Sleep Quality Index (PSQI) and Montreal Cognitive Assessment (MoCA). Data were entered in Microsoft Excel and analysed using IBM SPSS Statistics version 26.0. Descriptive statistics were used for demographic and categorical variables. Spearman’s rank correlation was used to examine the relationship between PSQI and MoCA scores. Results: The mean age was 21.77 ± 1.62 years. The largest screen-time category was 6–8 hours/day (35.25%). The mean PSQI score was 7.17 ± 3.13; 68.85% had mild sleep disturbance, 16.39% moderate sleep disturbance, 0.82% severe sleep disturbance and 13.93% good sleep quality. The mean MoCA score was 23.78 ± 2.19; 77.05% were classified as mild impairment and 22.95% as normal, with no participants classified as moderate or severe. A statistically significant negative correlation was found between PSQI and MoCA scores (ρ = −0.28, p = 0.002). Conclusion: In this sample, sleep disturbance and mild cognitive impairment were common. Higher PSQI scores were significantly associated with lower MoCA scores. Because the study was cross-sectional, these findings describe associations and do not establish causation.