The objective of the study was to examine the effects of perceived stress on depression and subsequently to examine the effects of depression on alcohol use disorders. The data were obtained by an electronic questionnaire survey during the coronavirus disease 2019 (COVID-19) pandemic ( n = 1523 Slovak university students). Descriptive, regression, and correlation analysis were used in the analytical processing, while the analyses included students’ scores in three diagnostic tools (Perceived Stress Scale (PSS), Patient Health Questionnaire for depression (PHQ 9), and Alcohol Use Disorders Identification Test (AUDIT)), as well as gender and income characteristics. The PSS identified an increased level of perceived stress in female students, while in contrast, the AUDIT showed an increased level of alcohol use disorders in male students. Differences in mental and behavioural disorders between the gender and income categories were significant in most of the analysed cases. In terms of gender-income characteristics, it was possible to confirm a significant positive effect of the PSS score on the PHQ 9 score, as well as a significant positive effect of the PHQ 9 score on the AUDIT score. As a result, efforts to reduce stress will be reflected in a reduction of depressive disorders as well as a reduction of excessive alcohol consumption among students.