Background: Occupational stress and burnout in the medical field are common factors that can have a negative impact on the quality of clinical care. In the Romanian healthcare environment, there exists important financial difficulties contributing additionally to stress in this study, we aimed to investigate if resilience and emotional intelligence would prove to be protective factors against stress. Methods: In our cross-sectional study, we investigated 189 medical professionals, using convenience sampling, from July 2022 to September 2022 in two university centers. We applied a self-reported questionnaire that included socio-demographic characteristics and three scales that measured perceived stress (the Perceived Stress Scale), resilience to stress (the Connor–Davidson Resilience Scale), and emotional intelligence (the short-form Trait Emotional Intelligence Questionnaire). Results: Age was positively associated with resilience levels, meaning that resilience increases with age. While specialist physicians had the highest emotional intelligence score, nurses and other healthcare workers had the highest resilience scores. Perceived stress level was negatively correlated with resilience to stress and with emotional intelligence levels. Resilience to stress was positively correlated with emotional intelligence. Conclusions: The major strength of this study is the finding that resilience to stress mediated the association between perceived stress and emotional intelligence. Because resilience is negatively associated with burnout, resilience to stress and emotional intelligence are potential targets for training aimed at improving the working environment and reducing current levels of burnout in the Romanian Health System and beyond.