Focusing on the moral hazard of third-party environmental service providers in monitoring and controlling the emission of pollutants by enterprises, this paper takes the third-party governance of environmental pollution under the incentive-and-constraint mechanism as its research object. It also constructs a game model involving emission-producing enterprises producing emissions, third-party environmental service providers, and local governments. Adopting this evolutionary game model, this paper analyzes the mechanism of local government’s role in effectively resolving the moral hazard between emission-producing enterprises producing emissions and third-party environmental service providers by exploring the conditions of spontaneous cooperation between emission-producing enterprises producing emissions and third-party environmental service providers. This paper provides a possible solution to the problem of emission-producing enterprises or third-party environmental service providers stealing and leaking emissions, as well as collusion between the two. The study presents two major findings. (1) There are three possible scenarios of breach of contract: unilateral breach by third-party environmental service providers, unilateral breach by emissions-producing enterprises, and collusion between the two. When a third-party environmental service provider unilaterally breaches a contract, emission-producing enterprises have regulatory responsibilities toward them. In such cases, local governments should reduce the penalties imposed on emission-producing enterprises. This measure would decrease the willingness of these enterprises to allocate a higher proportion of collusion payments to third-party environmental service providers. However, it would simultaneously provide a new avenue through which third-party environmental service providers would gain benefits, thereby increasing their expected gains from collusion. This would create a new game between the two parties, leading to the failure of collusion negotiations. (2) The efficacy of incentive-constraint mechanisms is influenced by the severity of contractual breaches, represented by the magnitude of stealing and leaking emissions. When false emissions reduction is at a high level, increasing the incentives for emission-producing enterprises and third-party environmental service providers cannot effectively prevent collusion; when the level is moderate, incentives for third-party environmental service providers can effectively prevent collusion, but incentives for emission-producing enterprises cannot; when the level is low, increasing the incentives for emission-producing enterprises and third-party environmental service providers can help prevent collusion. (3) When emission-producing enterprises engage in unilateral discharge, if a local government’s incentive for third-party environmental service providers exceeds the benefits it can obtain from regulating the discharged amount, third-party environmental service providers tacitly approve the company’s discharge behavior. However, with the strengthening of local government regulations, emission-producing enterprises tend to engage in more clandestine discharging of pollutants to obtain greater rewards. This practice infringes upon the revenue of third-party environmental service providers, as their earnings are positively correlated with the amount of pollution abated. Third-party environmental service providers no longer acquiesce to corporate emissions theft, resulting in an increase in the probability of the detection of emission-producing enterprises’ illicit discharges; in this way, the behavior of these enterprises is regulated.