The COVID-19 pandemic has created great uncertainty around the world, and due to the pandemic, nurses have been exposed to an increase in highly stressful clinical situations. This study examines the relationships between perceived stress and emotional disorders among nurses who have provided direct patient care during the COVID-19 pandemic and explores the mediating role of resilience in these relationships. In an online cross-sectional design, we asked Spanish nurses (N = 214) to complete self-reported scales, and we performed correlation and mediation analyses between perceived stress (Perceived Stress Scale, PSS-4), resilience (Wagnild Resilience Scale, RS-14), wellbeing (World Health Organization Wellbeing Index, five items, WHO-5), anxiety (PHQ-2) and depression (GAD-2). The nurses self-reported moderate levels of perceived stress, considerable psychological distress and high resilience. We found resilience to be significantly negatively correlated with the reported levels of perceived stress, anxiety and depression (p < 0.001). The mediating analysis revealed that resilience played a protective role in the direct relationships of stress with depression, anxiety, and psychological distress. To conclude, our findings supported the hypothesis that resilience mediated the relationship between stress and mental health.