This paper assesses the relational effects of perceived organizational support (POS), fear of COVID-19 (FOC-19), and work-related stress (WRS) on the safety performance of healthcare staff. The sample for this research was extracted from the University College Hospital (UCH) in the Oyo State of Nigeria. The participants were midwives, doctors, auxiliary services staff, and nurses who functioned in a COVID-19 hospital ward, fever or respiratory ICU, Auxiliary services, or outpatient clinics. This investigation espoused a clinical cross-sectional survey involving self-reported surveys. Of the 150 questionnaires distributed, 147 were fit for scrutiny and analyzed with Statistical Packages for the Social Sciences (SPSS version 28). This paper established a relationship between POS and safety performance (SP). Besides, it showed a significant positive correlation between FOC-19 and SP. It further noted that work-related stress negatively relates to safety performance. Moreover, this study showed the significant joint strong influence of POC, FOC-19, and WRS on the safety performance of healthcare workers. Hence, healthcare institutions are encouraged to create adequate support for healthcare workers, particularly during a global health crisis. Government and healthcare institutions should also develop an awareness program on the danger and consequences of getting infected by the virus or infecting other significant others. This will increase the fear of COVID-19 and, consequently, health workers’ safety performance. Besides, it is recommended that the management of healthcare institutions provides a proper work structure and schedule to help reduce workloads, consequently reducing WRS, as lowering it improves healthcare workers’ safety performance.