As coronavirus proliferation and death rates explode across the nation, the globe is on the verge of another health crisis, with daily doses of mental stress and depression among people of all ages. Our study was designed to investigate depression and stress among tertiary level students in Bangladesh during COVID-19 and to explore the influencing factors associated to them. We considered socio-demographics, educational information, financial information, life-style factors, and Depression Anxiety Stress Scale-21 etc. Univariate, bi-variate and binary logistic regression analysis was conducted. In our study, 32.6% (n=132) of the respondent were mentally depressed, and 44.9% (n=182) were stressed. Our analysis indicates that students aged more than 25 years, in a relationship, and those who ignored news were more likely to get depressed. Similarly, those who believed to have a hangout effect, ignored news, and spent more than 5 hours online daily were more likely to experience stress. On the other hand, students who are extrovert, participated in extra-curricular activities, did physical activities, meditated/prayed, solved problems, and studied more than 2 hours were less likely to get depressed. Likewise, students who were extrovert participated in physical activities and studied more than 2 hours were less likely to get stressed. We need to address students' mental health issues because of its long-lasting impact on current and future society, and make informed decisions to tackle depression and stress.