The frequent occurrence of transboundary environmental pollution incidents hinders the integrated development of the Yangtze River Delta region. The spillover effect of environmental pollution in the inter-governmental governance game has put local governments in a prisoner’s dilemma, resulting in a tendency for local governments to choose vicious competition strategies, while the central government’s intervention in the governance model is ineffective. Based on the theory of evolutionary game and governmental behavior, the Yangtze River Delta Transboundary Environmental Pollution Control Foundation was innovatively introduced. Together with provinces A and B, a tripartite evolutionary game model was constructed. The stability analysis and simulation of equilibrium points were carried out, the mechanism of intergovernmental behavior was clarified, and the effectiveness of the intervention of the Yangtze River Delta Transboundary Environmental Pollution Control Foundation was evaluated. The results show that the Yangtze River Delta Transboundary Environmental Pollution Control Foundation has significant advantages in terms of the effectiveness of game intervention and the speed of guidance and regulation, and has been effective in alleviating the problem of overreliance on administrative resources. Policy recommendations are proposed to introduce tripartite institutions to participate in governance, promote the decentralization of intergovernmental governance, and build an efficient coordination mechanism to achieve equal collaboration, complementary advantages, and mutual benefits.