Educational management and social psychology researchers have frequently suggested that job burnout and even turnover intention of college teachers can be induced by stress, which is an inherent part of fast-changing environments and advanced educational technology. However, studies about the contingency effect remain limited. We articulate the effect of role stress and technostress by integrating organizational behaviour and educational management literature. Particularly, this study tries to investigate the moderating effect of teacher agility and leader-member exchange differentiation on suppressing burnout. According to the job demands-resources model, we proposed that the negative effect of stress on burnout depends on the degree of agility and leader-member change quality (LMXD). A study of 271 samples supports the propositions. Specifically, the adverse effect of role stress on job burnout is strengthened by both employee agility and LMXD. We further elaborate theoretical implications on educational management, social psychology, and job demands-resources model.