Background: Job burnout has become a widespread phenomenon in school settings. However, little is known about the mental health condition of the growing cohort of generalist teachers in rural primary schools. Drawing on the job demands–resource model and social exchange theory, this study examines the correlation between job burnout and job satisfaction through perceived organizational support and work engagement. Methods: We recruited 639 Chinese generalist teachers in rural primary schools as the study subjects and developed a serial mediation model to assess the hypothesized construct. The data acquired online via Wenjuanxing Software were confirmed as valid and analyzed with SPSS and SmartPLS. Results: The participants scored above the median in perceived organizational support, work engagement, and job satisfaction, and had scores close to the median for job burnout. Statistically significant differences among the investigated variables were found in gender, age, experience, and degree. Job burnout was negatively predictive of perceived organizational support, work engagement, and job satisfaction (each p = 0.000). Perceived organizational support mediated the association between job burnout and work engagement (p = 0.000) and the connection between job burnout and job satisfaction (p = 0.000), while work engagement mediated the association between job burnout and job satisfaction (p = 0.000) and the association between perceived organizational support and job satisfaction (p = 0.000). Conclusions: Perceived organizational support and work engagement as two sequential mediators buffered the detrimental impact of job burnout on job satisfaction among Chinese generalist teachers in rural primary schools. Targeted strategies should be implemented to diminish generalist teachers’ feelings of burnout, being unsupported by organizations, disengagement at work, and dissatisfaction with the job.