As sports activities have recently become socio-culturally important in South Korea, the roles and functions of public sports organizations are attracting attention. In this situation, perceived organizational support is considered one of the significant variables to explain the attitudes and behaviors of employees within the organizations. Hence, the purpose of this study is to investigate the relationship between perceived organizational support of public sports organizations, work engagement, organizational citizenship behavior, and customer orientation and examine the mediating effect of work engagement. This study collected data from 248 employees working for public sports organizations, and data were analyzed with SPSS 26.0 and AMOS 26.0. The results showed the following. (1) Perceived organizational support has a significant positive effect on work engagement but does not affect organizational citizenship behavior and customer orientation. (2) Work engagement significantly positively affects organizational citizenship behavior and customer orientation. (3) Work engagement has been shown to fully mediate the relationship between perceived organizational support, organizational citizenship behavior, and customer orientation. This study suggests that public sports organizations need an efficient support strategy that can maximize employees’ work engagement. For example, organizations should increase their sense of unity with employees and understand the importance of their work to strengthen perceived organizational support. Lastly, organizations need to create an environment where employees can devote themselves to and focus on their work.