This study used conservation of resource theory and stress theory to examine the moderated effect of leader–member exchange (LMX) on the indirect relationship between customer incivility and deviant work behaviors (DWB) mediated by emotional exhaustion. Data were collected from the supervisor–employee dyads of 79 work units in Taiwan, including 79 supervisors and 328 employees. Statistical analyses were conducted using Mplus for model testing. The results show that emotional exhaustion mediated the relationship between customer incivility and DWB, and that LMX positively moderated the relationship between emotional exhaustion and DWB. The findings suggest that when employees are emotionally exhausted by customer incivility, a supervisor’s social support resources can significantly reduce their negative behaviors toward their colleagues.