Mining roadway is the main occurrence area of coal bursts in underground coal mining. A good understanding of the failure process of elastic zone and energy evolution inducing instability of support structure can offer useful insight into the coal burst mechanism. This study proposes a novel coal burst criterion of anchored roadway surrounding rock under dynamic disturbance through mechanical modeling. The coal burst hazard and its main controlling factors were studied based on case analysis, and then the application of novel criterion in coal burst prevention and control was clarified. Results show that the existence of residual energy Ur of elastic zone is a prerequisite for coal burst of the roadway. The roadway support with ultimate value Us of absorbed energy needs to resist and absorb the kinetic energy Uk released from a dynamic failure of elastic zone and the energy Up imposed by impact-induced convergence of surrounding rocks on a support system, and the novel coal burst criterion is proposed as Uk + Up > Us. Under the same support conditions, the roadway roof is more prone to dynamic failure. According to the influences of main controlling factors on coal burst hazard, the corresponding prevention and control measures can be taken from improvement for the anti-impact capability of support, pressure relief in surrounding rocks, reduction of dynamic-loading energy, and roadway restoration after coal burst.