Background Patient safety culture and patient safety competency could be associated with adverse events (AEs). This study aimed to investigate the associations between nurses’ perceptions of patient safety culture, patient safety competency, and AEs. Methods A cross-sectional study was carried out among 338 nurses employed in three university hospitals in Qom, Iran between 17 August 2021 and 12 November 2021. Data were collected using three questionnaires: patient safety culture, patient safety competency, and AEs. Data were analyzed using SPSS-21 software. A multiple logistic regression model was used to analyze the data. Results The results of this study showed that medication errors were significantly associated with “frequency of events reported” (OR = 0.706, P = 0.012), “supervisor/manager expectations and actions promoting patient safety” (OR = 0.733, P = 0.048), and “management support for patient safety” (OR = 0.755, P = 0.012). Pressure ulcers were significantly associated with “supervisor/manager expectations and actions promoting patient safety” (OR = 0.729, P = 0.039), “handoffs and transition” (OR = 0.707, P = 0.034), and “comfort speaking up about patient safety” (OR = 0.614, P = 0.016). Falls were significantly associated with “teamwork within units” (OR = 0.735, P = 0.031), “feedback and communication about error” (OR = 0.756, P = 0.046), and “handoffs and transition” (OR = 0.660, P = 0.012). The use of restraints for ≥8 hr. was significantly associated with “management support for patient safety” (OR = 0.701, P = 0.021). Conclusions According to the results of this study, AEs are associated with some dimensions of patient safety culture and patient safety competency. Further research is needed to confirm these findings and identify interventions to reduce the occurrence of AEs.