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Introduction: There is a complex interaction between poor sleep quality, Internet addiction (IA), and depression. This study aimed to determine whether sleep quality or IA statistically mediates the association between the other two variables. Materials and Methods: This cross-sectional study was conducted from June 2022 to October 2022 in a medical college in Ajmer, Rajasthan. Data were collected from 400 undergraduate medical students. Data were collected using Depression, Anxiety, and Stress Scale-21, Pittsburgh Sleep Quality Index, and Young's IA tools. Data were analyzed by multivariate logistic regression and the PROCESS program in SPSS 20.0. Results: The mean (standard deviation) age of the students was 20.9 (1.68) years. About 43% of students (n = 174) had depression, 40.3% (n = 161) had poor sleep, and 54% (n = 216) had IA. The age of the students (adjusted odds ratio [aOR] = 1.92), screen time per day (aOR = 1.06), smoking (aOR = 13.20), sleep quality (aOR = 1.16), and IA (aOR = 11.64) were significantly associated with depression. IA mediated 30.55% of the indirect effect of sleep quality on depression, whereas sleep quality mediated 18.18% of the indirect effect of IA on depression. Conclusion: Sleep quality and IA have a differential independent indirect effect on the association between depression and the other variable. Programs and counseling sessions that promote mental health should also address the adverse impact of poor sleep and IA.