Students play a key role in university social responsibility (USR), as they are the protagonists of change and the fundamental axis in the teaching-learning process. This study aims to assess the factors associated with the perception of university social responsibility among dental students from two universities in the Peruvian capital. This analytical cross-sectional study assessed 754 students from two Peruvian universities between May and July 2023. The study utilized a validated 51-item questionnaire to assess sociodemographic factors and dental students’ perception of USR. A Poisson regression model with robust variance and prevalence ratio (PR) was used to assess the influence of variables such as age, sex, marital status, type of university, academic year, and awareness of taking subjects related to USR. The significance was set at p < 0.05. The perception of USR was rated as poor, fair, and good by 16%, 67%, and 17% of the participants, respectively. According to the study, dental students from public universities were 68% more likely to perceive their USR education as poor than those from private universities (APR = 1.68, 95% CI: 1.06–2.66), and those who were aware of taking MSR-related courses were 37% less likely to perceive their USR education as poor (APR = 0.63, 95% CI: 0.40–0.98). Similarly, dental students attending public universities were 2.28 times more likely to perceive poor organizational management in USR compared to their counterparts at private universities (APR = 2.28, 95% CI: 1.51–3.44). Additionally, students in their first and second academic years were 62% and 57% less likely to perceive poor organizational management in USR compared to those in their sixth year (APR = 0.38, 95% CI: 0.19–0.79 and APR = 0.43, 95% CI: 0.20–0.95; respectively). Furthermore, students from public universities were 2.31 times more likely to perceive social participation in USR poorly compared to their counterparts from private universities (APR = 2.31, 95% CI: 1.63–3.26). Lastly, it was observed that students from public universities were 2.51 times more likely to have a poor overall perception of USR compared to students from private universities (APR = 2.51, 95% CI: 1.67–3.78). Acknowledging the diverse contexts and challenges inherent in public and private institutions, it can be concluded that more than half of the dental students had a fair perception of USR. Additionally, attending a public university was found to be a risk factor for having a poor perception of USR. However, taking a course related to USR and being in the early years of the program were identified as protective factors against a poor perception of organizational training and management in USR. It is recommended that students be involved in USR activities, including the Sustainable Development Goals, from the first years of their university education, especially in public universities.